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ANNEXES Annex A: Checkings of pillars, beams and crosses Pillars Beams Crosses Annex B: Plans of portics and joints Annex C: Checkings of Joints Annex D: Checking and verification efforts in the shoe Annex E: Plans of the building ANNEX A: Checkings of pillars, beams and crosses Legend ᵝ: Buckling coefficient LK: Buckling length (m) Cm: Moment coefficient Nt: Tensile Nc: Resistance to compression MY: Flexion strength Y MZ: Flexion strength Z VY: Shear strength Y VZ: Shear strength Z MYVZ: Resistance to bending moment Y and Z combined shear MZVY: Resistance to bending moment Z and Y combined shear NMYMZ: Resistance to bending and combined axial NMYMZVYVZ: Resistance to bending, shear and combined axial Mt: Torsional strength MtVZ: Shear resistance and torque combined Z MtVY: Shear resistance and torque combined Y : Limiting slenderness x: Distance from the origin of the bar ƞ: Utilization rate (%) Pillars........................................................................................................... 2 Beams.......................................................................................................... 37 Crosses ....................................................................................................... 72 PILLARS PILLAR 1 Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 83 . 469 t Must be satisfied: 0 . 110 1 N r , Rd 756 . 881 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (3). Nt,Ed: Axial traction applicant bad calculation = 83.469 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 270.0 cm2 · 2803.26 kp/cm2 = 756.881 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: 3 N c , Ed 127.298 t 0 . 168 1 N c , Rd 756.881 t N c , Ed 127.298 t 0 . 770 1 N b , Rd 165.426 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·Q1 +1.5·V1 (4) +1.05·N1. Nc,Ed: Axial compression applicant bad calculation = 127.298 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 270.0 cm2 · 2803.26 kp/cm2 = 756.881 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 2 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) The resistance of buckling Nb,Rd compressed in a bar is given by: Nb,Rd = χ ·A · fyd = 0.22 · 270.0 cm2 · 2803.26 kp/cm2 = 165.426 t Where: A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 χ: Reduction coefficient for buckling. 1 0.91 ( y) and 0.22( z ) ≤ 1 ( ) 2 2 Where: 0 . 5· 1 · 0 . 2 ( ) 2 = 0.69 ( y) and 2.70( z). α: Reduction coefficient for buckling.= 0.21(αy) and 0.34(αz). 4 A· f y : Reduced slenderness = 0.55 ( y ) and 1.95 ( z ). N cr Ncr: Elastic critical elastic buckling. = 198.511 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 2508.902 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 198.511 t L kz c) Elastic critical axial buckling torque. 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: Iy: Moment of inertia of the gross section with the axis Y = 171000.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 13530.00 cm4 It: Moment of inertia of uniform torsion = 667.20 cm4 Iw: constant warping of the section = 10970000.00 cm6 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 Lky: effective length for buckling with the axis Y. = 12 m Lkz: effective length for buckling with the axis Z. = 12 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 26.14 cm io (i y i z y 0 z 0 ) ( 25 ,17 7 . 08 0 0 ) 26 . 14 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 25.17 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.08 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 1 0 7 . 313 t ·m Ed 0 . 596 1 M c , Rd 1 8 0 . 110 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1(2) Where: 5 MEd: Bending moment calculation applicant awful = 107.313 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 180.110 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 6425.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 1 . 042 t ·m Ed 0 . 027 1 M c , Rd 38 . 993 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1 (1) +1.05·N1 Where: MEd: Bending moment calculation applicant awful = 1.042 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 38.993 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1391.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 17 . 198 t 0 . 114 1 V c , Rd 150 . 517 t Where: VEd: Applicant for calculating shear badly. = 17.198 t The shear resistance of calculating VcRd is given by: f yd VCRd = A v 150.517 t 3 Where: Av: Cross-cutting area = h · tw = 93.00 cm2 6 h: Song of the section. = 600 mm tw: Web thickness. = 15.5 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 34.84 < 55.46 tw Where: d λw: Slenderness of the soul.= = 34.84 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 0 . 171 t 0 . 001 1 V c , Rd 301 . 520 t Where: VEd: Applicant for calculating shear badly. = 0.171 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 301.520 t 3 Where: Av: Cross-cutting area = A - d · tw = 186.30 cm2 A: Gross sectional area.= 270.0 cm2 d: Web depth. = 540 mm tw: Web thickness. = 15.5 mm 7 Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 17.198 ≤ 75.259 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(2). Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 0.171 ≤ 150.760 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(1)+1.05·N1. Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.030 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.343 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.846 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(1)+1.05·N1 Where: Nc,Ed: Axil applicant compression calculation. = 127.298 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. 8 Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 2 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 179 . 781 tm M pl , Rd , y 180 . 110 tm 1 0 . 5·a na 2 na M N , Rd , z M pl , Rd , z ·1 =38.993 tm 1 a 2 5·n 5 1 N c , Ed n 0 . 168 1 N pl , Rd Npl,Rd: compressive strength of the gross section.= 756.881 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (180.110 tm and 38.993 tm) A 2·b·t f a 0 . 33 0 . 5 A A: Area of the gross section. = 270.0 cm2 b: width of the wing. = 30 cm tf: thickness of the wing = 30 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 067 tm 0 . 019 1 M T , Rd 3 . 599 tm Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(2). MT,Ed: torque calculation applicant awful.= 0.067 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 3.599 t m 3 Where: WT: Torsional modulus. = 222.40 cm3 9 PILLAR 2 Tensile (Eurocode 3 EN 1993-1-1): This colum is not working in Tensile strength. Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 20.504 t 0 . 027 1 N c , Rd 756.881 t N c , Ed 20.504 t 0 . 124 1 N b , Rd 165.426 t The calculation effort lousy applicant occurs for the combination of actions G +0.9·V1 (1) +1.5·N1. Nc,Ed: Axial compression applicant bad calculation = 20.504 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 270.0 cm2 · 2803.26 kp/cm2 = 165.426 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 2 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) The resistance of buckling Nb,Rd compressed in a bar is given by: Nb,Rd = χ ·A · fyd = 0.22 · 270.0 cm2 · 2803.26 kp/cm2 = 165.426 t Where: A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 10 χ: Reduction coefficient for buckling. 1 0.91 ( y) and 0.22( z ) ≤ 1 ( ) 2 2 Where: 0 . 5· 1 · 0 . 2 ( ) 2 = 0.69 ( y) and 2.70( z). α: Reduction coefficient for buckling.= 0.21(αy) and 0.34(αz). A· f y : Reduced slenderness = 0.55 ( y ) and 1.95 ( z ). N cr Ncr: Elastic critical elastic buckling. = 198.511 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 2508.902 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 198.511 t L kz c) Elastic critical axial buckling torque. 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: Iy: Moment of inertia of the gross section with the axis Y = 171000.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 13530.00 cm4 It: Moment of inertia of uniform torsion = 667.20 cm4 Iw: constant warping of the section = 10970000.00 cm6 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 Lky: effective length for buckling with the axis Y. = 12 m Lkz: effective length for buckling with the axis Z. = 12 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 26.14 cm io (i y i z y 0 z 0 ) ( 25 . 17 7 . 08 0 0 ) 26 . 14 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 25.17 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.08 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. 11 Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 1 5 9 . 852 t ·m Ed 0 . 888 1 M c , Rd 180 . 110 t ·m The calculation effort lousy applicant occurs for the combination of G+1.5·V1 (3) +1.05·N1 Where: MEd: Bending moment calculation applicant awful = 159.852 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 180.110 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 6425.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 10 . 460 t ·m Ed 0 . 268 1 M c , Rd 38 . 993 t ·m The calculation effort lousy applicant occurs for the combination of 1.35G + 1.5·V1(4). Where: MEd: Bending moment calculation applicant awful = 10.460 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 38.993 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1391.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: 12 V Ed 19 . 511 t 0 . 130 1 V c , Rd 150 . 517 t Where: VEd: Applicant for calculating shear badly. = 19.511 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 150.517 t 3 Where: Av: Cross-cutting area = h · tw = 93 cm2 h: Song of the section. = 600 mm tw: Web thickness. = 15.5 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 34.84 < 55.46 tw Where: d λw: Slenderness of the soul.= = 34.84 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 1 . 682 t 0 . 006 1 V c , Rd 301 . 520 t Where: VEd: Applicant for calculating shear badly. = 1.682 t 13 The shear resistance of calculating V cRd is given by: f yd VCRd = A v 301.520 t 3 Where: Av: Cross-cutting area = A - d · tw = 186.30 cm2 A: Gross sectional area.= 270 cm2 d: Web depth. = 540 mm tw: Web thickness. = 15.5 mm Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 19.511 ≤ 75.259 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(3)+1.05·N1. Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 1.682 ≤ 150.760 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.788≤ 1 M N , Rd , y M N , Rd , z 14 N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.936 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.577 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(3)+1.05·N1 Where: Nc,Ed: Axil applicant compression calculation. = 17.646 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 180 . 110 tm M pl , Rd , y 180 . 110 tm 1 0 . 5·a na 2 na M N , Rd , z M pl , Rd , z ·1 =38.993 tm 1 a 2 5·n 5 1 N c , Ed n 0 . 023 1 N pl , Rd Npl,Rd: compressive strength of the gross section.= 756.881 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (180.110 tm and 38.993 tm) A 2·b·t f a 0 . 33 0 . 5 A A: Area of the gross section. = 270.0 cm2 b: width of the wing. = 30.0 cm tf: thickness of the wing = 30.0 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 011 tm 0 . 003 1 M T , Rd 3 . 599 tm 15 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(2)+1.05·N1 MT,Ed: torque calculation applicant awful.= 0.011 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 3.599 t m 3 Where: WT: Torsional modulus. = 222.40 cm3 PILLAR 3 Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 0 . 285 t Must be satisfied: 0 . 001 1 N r , Rd 756 . 881 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (4). Nt,Ed: Axial traction applicant bad calculation = 0.285 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 270.0 cm2 · 2803.26 kp/cm2 = 756.881 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 20.959 t 0 . 028 1 N c , Rd 756.881 t N c , Ed 20.959 t 0 . 078 1 N b , Rd 269.171 t 16 The calculation effort lousy applicant occurs for the combination of actions 1.35·G +0.9·V1 (2) +1. 5·N1. Nc,Ed: Axial compression applicant bad calculation = 20.959 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 270.0 cm2 · 2803.26 kp/cm2 = 756.881 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 2 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) The resistance of buckling Nb,Rd compressed in a bar is given by: Nb,Rd = χ ·A · fyd = 0.36 · 270.0 cm2 · 2803.26 kp/cm2 = 269.171 t Where: A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 χ: Reduction coefficient for buckling. 1 0.95( y) and 0.36( z ) ≤ 1 ( ) 2 2 Where: 0 . 5· 1 · 0 . 2 ( ) 2 = 0.61 ( y) and 1.79( z). α: Reduction coefficient for buckling.= 0.21(y) and 0.34(z) A· f y : Reduced slenderness = 0.41( y ) and 1.46 ( z ). N cr Ncr: Elastic critical elastic buckling. = 236.24 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. 17 ·E ·I y 2 N cr , y 2 2869.85 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 236.24 t L kz c) Elastic critical axial buckling torque. 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: Iy: Moment of inertia of the gross section with the axis Y = 171000.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 13530.00 cm4 It: Moment of inertia of uniform torsion = 667.20cm4 Iw: constant warping of the section = 10970000.00 cm6 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 Lky: effective length for buckling with the axis Y. = (11·1,02) m Lkz: effective length for buckling with the axis Z. = 11 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 21.21 cm io (i y i z y 0 z 0 ) ( 25 . 17 7 . 08 0 0 ) 26 . 14 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 25.17 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.08 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 61.058 t ·m Ed 0 . 339 1 M c , Rd 1 8 0 . 110 t ·m The calculation effort lousy applicant occurs for the combination of 1.35 G +1.5·V1(2) +1.05N1 Where: MEd: Bending moment calculation applicant awful = 61.058 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 180.110 t·m Where: 18 Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 6425.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 1 . 926 t ·m Ed 0 . 049 1 M c , Rd 38 . 993 t ·m The calculation effort lousy applicant occurs for the combination of 1.35G +1.5·V1 (1). Where: MEd: Bending moment calculation applicant awful = 1.926 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 38.993 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1391.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 8 . 007 t 0 . 053 1 V c , Rd 150 . 517 t Where: VEd: Applicant for calculating shear badly. = 8.007 t The shear resistance of calculating VcRd is given by: f yd VCRd = A v 150.517 t 3 Where: Av: Cross-cutting area = h · tw = 93 cm2 h: Song of the section. = 600 mm tw: Web thickness. = 15.5 mm 19 Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 34.84 < 55.46 tw Where: d λw: Slenderness of the soul.= = 34.84 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 0 . 363 t 0 . 001 1 V c , Rd 301 . 520 t Where: VEd: Applicant for calculating shear badly. = 0.393 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 301.520 t 3 Where: Av: Cross-cutting area = A - d · tw = 186.30 cm2 A: Gross sectional area.= 270 cm2 d: Web depth. = 540 mm tw: Web thickness. = 15.5 mm 20 Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 8.007 ≤ 75.259 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(4). Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 0.393 ≤ 150.760 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(1). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.116 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.367 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.241 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(2)+1.05·N1 Where: Nc,Ed: Axil applicant compression calculation. = 16.661 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. 21 Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 180 . 110 tm M pl , Rd , y 180 . 110 tm 1 0 . 5·a na 2 na M N , Rd , z M pl , Rd , z ·1 =38.993 tm 1 a 2 5·n 0 . 11 1 N c , Ed n 0 . 022 N pl , Rd Npl,Rd: compressive strength of the gross section.= 756.881 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (180.110 tm and 38.993tm) A 2·b·t f a 0 . 33 0 . 5 A A: Area of the gross section. = 270 cm2 b: width of the wing. = 30 cm tf: thickness of the wing = 30 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 013 tm 0 . 009 1 M T , Rd 3 . 599 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(4). MT,Ed: torque calculation applicant awful.= 0.033 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 3.599 t m 3 Where: WT: Torsional modulus. = 222.40 cm3 22 PILLAR 4 Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 53 . 811 t Must be satisfied: 0 . 071 1 N r , Rd 756 . 881 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (2). Nt,Ed: Axial traction applicant bad calculation = 53.811 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 270.0 cm2 · 2803.26 kp/cm2 = 756.881 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 93.711 t 0 . 124 1 N c , Rd 756.881 t N c , Ed 93.711 t 0 . 566 1 N b , Rd 165.426 t The calculation effort lousy applicant occurs for the combination of actions 1.35·G +1.5·V1 (4) +1. 05·N1. Nc,Ed: Axial compression applicant bad calculation = 93.711 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 270.0 cm2 · 2803.26 kp/cm2 = 756.881 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 2 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 23 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) The resistance of buckling Nb,Rd compressed in a bar is given by: Nb,Rd = χ ·A · fyd = 0.22 · 270.0 cm2 · 2803.26 kp/cm2 = 165.426 t Where: A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 χ: Reduction coefficient for buckling. 1 0.91( y) and 0.22( z ) ≤ 1 ( ) 2 2 Where: 0 . 5· 1 · 0 . 2 ( ) 2 = 0.69 ( y) and 2.70( z). α: Reduction coefficient for buckling.= 0.21(y) and 0.34(z) A· f y : Reduced slenderness = 0.55( y ) and 1.95( z ). N cr Ncr: Elastic critical elastic buckling. = 198.511 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 2508.902 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 198.511 t L kz c) Elastic critical axial buckling torque. 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: Iy: Moment of inertia of the gross section with the axis Y = 171000.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 13530.00 cm4 It: Moment of inertia of uniform torsion = 667.20cm4 Iw: constant warping of the section = 10970000.00 cm6 24 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 Lky: effective length for buckling with the axis Y. = 12 m Lkz: effective length for buckling with the axis Z. = 12 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 21.21 cm io (i y i z y 0 z 0 ) ( 25 . 17 7 . 08 0 0 ) 26 . 14 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 25.17 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.08 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 136.965 t ·m Ed 0 . 760 1 M c , Rd 1 8 0 . 110 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1(1). Where: MEd: Bending moment calculation applicant awful = 136.965 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 180.110 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 6425.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 1 . 926 t ·m Ed 0 . 012 1 M c , Rd 38 . 993 t ·m The calculation effort lousy applicant occurs for the combination of 1.35G +1.5·V1 (4)+1.05N1. Where: MEd: Bending moment calculation applicant awful = 1.926 t·m 25 The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 38.993 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1391.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 23 . 268 t 0 . 155 1 V c , Rd 150 . 517 t Where: VEd: Applicant for calculating shear badly. = 23.268 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 150.517 t 3 Where: Av: Cross-cutting area = h · tw = 93 cm2 h: Song of the section. = 600 mm tw: Web thickness. = 15.5 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 34.84 < 55.46 tw Where: d λw: Slenderness of the soul.= = 34.84 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy 26 fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 0 . 076 t 0 . 001 1 V c , Rd 301 . 520 t Where: VEd: Applicant for calculating shear badly. = 0.393 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 301.520 t 3 Where: Av: Cross-cutting area = A - d · tw = 186.30 cm2 A: Gross sectional area.= 270 cm2 d: Web depth. = 540 mm tw: Web thickness. = 15.5 mm Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 23.268 ≤ 75.259 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(1). Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 0.076 ≤ 150.760 2 27 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05N1. Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.563 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.837 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.609 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(1)+1.05·N1 Where: Nc,Ed: Axil applicant compression calculation. = 33.802 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 180 . 110 tm M pl , Rd , y 180 . 110 tm 1 0 . 5·a na 2 na M N , Rd , z M pl , Rd , z ·1 =38.993 tm 1 a 2 5·n 0 . 225 1 N c , Ed n 0 . 045 N pl , Rd Npl,Rd: compressive strength of the gross section.= 756.881 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (180.110 tm and 38.993tm) A 2·b·t f a 0 . 33 0 . 5 A 28 A: Area of the gross section. = 270 cm2 b: width of the wing. = 30 cm tf: thickness of the wing = 30 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 049 tm 0 . 014 1 M T , Rd 3 . 599 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(1). MT,Ed: torque calculation applicant awful.= 0.049 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 3.599 t m 3 Where: WT: Torsional modulus. = 222.40 cm3 PILLAR 5 Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 8 . 681 t Must be satisfied: 0 . 011 1 N r , Rd 756 . 881 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (3)+1.05N1. Nt,Ed: Axial traction applicant bad calculation =8.681 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 270.0 cm2 · 2803.26 kp/cm2 = 756.881 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 29 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 16.181 t 0 . 021 1 N c , Rd 756.881 t N c , Ed 16.181 t 0 . 084 1 N b , Rd 192.643 t The calculation effort lousy applicant occurs for the combination of actions 1.35·G +1.5·V1 (1). Nc,Ed: Axial compression applicant bad calculation = 16.181 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 270.0 cm2 · 2803.26 kp/cm2 = 756.881 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 2 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) The resistance of buckling Nb,Rd compressed in a bar is given by: Nb,Rd = χ ·A · fyd = 0.25 · 270.0 cm2 · 2803.26 kp/cm2 = 192.643 t Where: A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 χ: Reduction coefficient for buckling. 1 0.92( y) and 0.25( z ) ≤ 1 ( ) 2 2 Where: 0 . 5· 1 · 0 . 2 ( ) 2 = 0.66 ( y) and 2.37( z). 30 α: Reduction coefficient for buckling.= 0.21(y) and 0.34(z) A· f y : Reduced slenderness = 0.50( y ) and 1.79 ( z ). N cr Ncr: Elastic critical elastic buckling. = 236.245 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 2985.800 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 236.245 t L kz c) Elastic critical axial buckling torque. 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: Iy: Moment of inertia of the gross section with the axis Y = 171000.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 13530.00 cm4 It: Moment of inertia of uniform torsion = 667.20cm4 Iw: constant warping of the section = 10970000.00 cm6 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 Lky: effective length for buckling with the axis Y. = 11 m Lkz: effective length for buckling with the axis Z. = 11 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 21.21 cm io (i y i z y 0 z 0 ) ( 25 . 17 7 . 08 0 0 ) 26 . 14 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 25.17 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.08 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 11.297 t ·m Ed 0 . 063 1 M c , Rd 1 8 0 . 110 t ·m 31 The calculation effort lousy applicant occurs for the combination of 1.35 G +1.5·V1(1). Where: MEd: Bending moment calculation applicant awful = 11.297 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 180.110 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 6425.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 9 . 276 t ·m Ed 0 . 238 1 M c , Rd 38 . 993 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1 (4). Where: MEd: Bending moment calculation applicant awful = 9.276 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 38.993 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1391.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 1 . 974 t 0 . 013 1 V c , Rd 150 . 517 t Where: VEd: Applicant for calculating shear badly. = 1.974 t The shear resistance of calculating VcRd is given by: 32 f yd VCRd = A v 150.517 t 3 Where: Av: Cross-cutting area = h · tw = 93 cm2 h: Song of the section. = 600 mm tw: Web thickness. = 15.5 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 34.84 < 55.46 tw Where: d λw: Slenderness of the soul.= = 34.84 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 4 . 917 t 0 . 016 1 V c , Rd 301 . 520 t Where: VEd: Applicant for calculating shear badly. = 4.917 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 301.520 t 3 Where: Av: Cross-cutting area = A - d · tw = 186.30 cm2 33 A: Gross sectional area.= 270 cm2 d: Web depth. = 540 mm tw: Web thickness. = 15.5 mm Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 1.974 ≤ 75.259 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(1). Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 3.792 ≤ 150.760 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05N1. Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.238 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.238 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.238 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions G+1.5·V1(4). 34 Where: Nc,Ed: Axil applicant compression calculation. = 16.661 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 180 . 110 tm M pl , Rd , y 180 . 110 tm 1 0 . 5·a na 2 na M N , Rd , z M pl , Rd , z ·1 =38.993 tm 1 a 2 5·n 0 . 005 1 N c , Ed n 0 . 001 N pl , Rd Npl,Rd: compressive strength of the gross section.= 756.881 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (180.110 tm and 38.993tm) A 2·b·t f a 0 . 33 0 . 5 A A: Area of the gross section. = 270 cm2 b: width of the wing. = 30 cm tf: thickness of the wing = 30 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 010 tm 0 . 003 1 M T , Rd 3 . 599 tm Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(2)+1.05N1. MT,Ed: torque calculation applicant awful.= 0.010 t m The resistant torque calculation MT,Rd is given by: 35 1 M T , Rd ·W T · f yd 3.599 t m 3 Where: WT: Torsional modulus. = 222.40 cm3 36 BEAMS BEAM 1 Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 0 . 568 t Must be satisfied: 0 . 001 1 N t , Rd 756 . 881 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (1). Nt,Ed: Axial traction applicant bad calculation = 0.568 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 270.00 cm2 · 2803.26 kp/cm2 = 756.881 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: 37 N c , Ed 6.008 t 0 . 008 1 N c , Rd 756.881 t The calculation effort lousy applicant occurs for the combination of actions 1.35·G+1.5·V1 (3) +1.05·N1. Nc,Ed: Axial compression applicant bad calculation = 6.008 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 270.00 cm2 · 2803.26 kp/cm2 = 756.881 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 2 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) If the slenderness ratio is λ≤0.2 or NC,Ed / Ncr ≤ 0.04 you can ignore the effect of buckling, and see only the cross section resistance. Where: N C , Ed 0 . 013 N Cr A· f y : Reduced slenderness = 1.28 N cr Ncr: Elastic critical elastic buckling. = 460.942 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 5825.658 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 469.942 t L kz c) Elastic critical axial buckling torque. 38 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: Iy: Moment of inertia of the gross section with the axis Y = 171000.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 13530.00 cm4 It: Moment of inertia of uniform torsion = 667.20 cm4 Iw: constant warping of the section = 10970000.00 cm6 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 Lky: effective length for buckling with the axis Y. =7.875 m Lkz: effective length for buckling with the axis Z. = 7.875 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 26.55 cm io (i y i z y 0 z 0 ) ( 25 ,17 7 . 08 0 0 ) 26 . 14 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 25.17 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.08 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 31 . 856 t ·m Ed 0 . 177 1 M c , Rd 180 . 110 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G +1.5·V1 (2) +1.05·N1 Where: MEd: Bending moment calculation applicant awful = 31.856 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 180.110 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 6425.00 cm3 39 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 36 . 397 t ·m Ed 0 . 933 1 M c , Rd 38 . 993 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G +1.5·V1 (3) +1.05·N1 Where: MEd: Bending moment calculation applicant awful = 36.397 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 38.993 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1391.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 8 . 051 t 0 . 053 1 V c , Rd 150 . 517 t Where: VEd: Applicant for calculating shear badly. = 8.051 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 150.517 t 3 Where: Av: Cross-cutting area = h · tw = 93.00 cm2 h: Song of the section. = 600 mm tw: Web thickness. = 15.5 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: 40 d 72 · 34.84 < 55.46 tw Where: d λw: Slenderness of the soul.= = 34.84 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 14 . 250 t 0 . 047 1 V c , Rd 301 . 520 t Where: VEd: Applicant for calculating shear badly. = 14.250 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 301.520t 3 Where: Av: Cross-cutting area = A - d · tw = 186.30 cm2 A: Gross sectional area.= 270.00 cm2 d: Web depth. = 540 mm tw: Web thickness. =15.5 mm Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. 41 V cRd V ED 8.051 ≤ 75.259 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05·N1. Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 3.400 ≤ 150.760 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(3)+1.05·N1. Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.935 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.699 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.976 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(3)+1.05·N1 Where: Nc,Ed: Axil applicant compression calculation. = 6.008 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 180 . 110 tm M pl , Rd , y 180 . 110 tm 1 0 . 5·a 42 na 2 na M N , Rd , z M pl , Rd , z ·1 =38.993 tm 1 a 2 5·n 0 . 004 1 N c , Ed n 0 . 008 N pl , Rd Npl,Rd: compressive strength of the gross section.= 756.881 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (180.110 tm and 38.993 tm) A 2·b·t f a 0 . 33 0 . 5 A A: Area of the gross section. = 270.00 cm2 b: width of the wing. = 30.00 cm tf: thickness of the wing = 30.00 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 022 tm 0 . 006 1 M T , Rd 3 . 599 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(3). MT,Ed: torque calculation applicant awful.= 0.022 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 3.599t m 3 Where: WT: Torsional modulus. = 222.40 cm3 Z shear resistance and torque combined (EN 1993-1-1 Eurocode 3: 2005) V Ed 8 . 051 t 0 . 053 1 V pl ,T , Rd 150 . 506 t Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05·N1. VEd: Applicant for calculating shear bad.= 8.051 t MT,Ed: Torque calculation applicant awful.= 0.001 t·m 43 The shear resistance reduced calculation Vpl, T, Rd is given by: T , Ed V pl ,T , Rd 1 ·V pl , Rd 150 . 506 t f yd 1 . 25 · 3 Where: Vpl, Rd: Shear resistance of calculation = 150.517 t M T , Ed τT, Ed: Shear stresses due to torsion = 0 . 31 kN 2 Wt cm WT: Module torsional strength = 222.40 cm3 BEAM 2 Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 3 . 918 t Must be satisfied: 0 . 007 1 N t , Rd 554 . 485 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (4). Nt,Ed: Axial traction applicant bad calculation = 3.918 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 197.80 cm2 · 2803.26 kp/cm2 = 554.485 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 17.029 t 0 . 031 1 N c , Rd 554.485 t The calculation effort lousy applicant occurs for the combination of actions 1.35·G+1.5·V1 (2) +1.05·N1. Nc,Ed: Axial compression applicant bad calculation = 17.029 t 44 The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 197.80 cm2 · 2803.26 kp/cm2 = 554.485 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 1 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) If the slenderness ratio is λ≤0.2 or NC,Ed / Ncr ≤ 0.04 you can ignore the effect of buckling, and see only the cross section resistance. Where: N C , Ed 0 . 022 N Cr A· f y : Reduced slenderness = 0.84 N cr Ncr: Elastic critical elastic buckling. = 791.188 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 4217.771 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 791.188 t L kz c) Elastic critical axial buckling torque. 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: Iy: Moment of inertia of the gross section with the axis Y = 57680.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 10820.00 cm4 It: Moment of inertia of uniform torsion = 355.70 cm4 Iw: constant warping of the section = 3817000.00 cm6 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 45 Lky: effective length for buckling with the axis Y. =5.375 m Lkz: effective length for buckling with the axis Z. = 5.375 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 18.61 cm io (i y i z y 0 z 0 ) (17 , 08 7 . 40 0 0 ) 18 . 61 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 17.08 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.40 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 10 . 415 t ·m Ed 0 . 214 1 M c , Rd 90 . 601 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G +1.5·V1 (1) +1.05·N1 Where: MEd: Bending moment calculation applicant awful = 10.415 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 90.601 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 3232.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 21 . 666 t ·m Ed 0 . 700 1 M c , Rd 30 . 948 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1 (2). Where: MEd: Bending moment calculation applicant awful = 21.666 t·m 46 The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 30.948 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1104.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 7 . 457 t 0 . 085 1 V c , Rd 87 . 397 t Where: VEd: Applicant for calculating shear badly. = 7.457 t The shear resistance of calculating VcRd is given by: f yd Vc,Rd = A v 87.397 t 3 Where: Av: Cross-cutting area = h · tw = 54.00 cm2 h: Song of the section. = 400 mm tw: Web thickness. = 13.5 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 26.07 < 55.46 tw Where: d λw: Slenderness of the soul.= = 26.07 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy 47 fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 7 . 259 t 0 . 030 1 V c , Rd 243 . 223 t Where: VEd: Applicant for calculating shear badly. = 7.259 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 243.223t 3 Where: Av: Cross-cutting area = A - d · tw = 150.28 cm2 A: Gross sectional area.= 197.80 cm2 d: Web depth. = 352 mm tw: Web thickness. =12.5 mm Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 6.486 ≤ 43.699 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(1) Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 7.259 ≤ 121.611 2 48 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(2). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.690 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.525 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.737 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(2)+1.05·N1 Where: Nc,Ed: Axil applicant compression calculation. = 17.029 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 90 . 601 tm M pl , Rd , y 90 . 601 tm 1 0 . 5·a na 2 na M N , Rd , z M pl , Rd , z ·1 =30.948 tm 1 a 2 5·n 0 . 155 1 N c , Ed n 0 . 031 N pl , Rd Npl,Rd: compressive strength of the gross section.= 554.485 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (90.601 tm and 30.948 tm) A 2·b·t f a 0 . 27 0 . 5 A 49 A: Area of the gross section. = 197.80 cm2 b: width of the wing. = 30.00 cm tf: thickness of the wing = 24.00 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 013 tm 0 . 005 1 M T , Rd 2 . 399 tm Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(2)+1.05N1. MT,Ed: torque calculation applicant awful.= 0.013 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 2.399t m 3 Where: WT: Torsional modulus. = 148.21 cm3 Z shear resistance and torque combined (EN 1993-1-1 Eurocode 3: 2005) V Ed 0 . 587 t 0 . 007 1 V pl ,T , Rd 87 . 296 t Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05·N1. VEd: Applicant for calculating shear bad.= 0.587 t MT,Ed: Torque calculation applicant awful.= 0.007 t·m The shear resistance reduced calculation Vpl, T, Rd is given by: T , Ed V pl ,T , Rd 1 ·V pl , Rd 87 . 296 t f yd 1 . 25 · 3 Where: Vpl, Rd: Shear resistance of calculation = 87.397 t M T , Ed τT, Ed: Shear stresses due to torsion = 4 . 67 kN 2 Wt cm WT: Module torsional strength = 148.21 cm3 50 BEAM 3 Tensile (Eurocode 3 EN 1993-1-1): The check was not necessary, since there is no axial traction Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 9.976 t 0 . 013 1 N c , Rd 756.881 t The calculation effort lousy applicant occurs for the combination of actions 1.35·G+1.5·V1(1) +1.05·N1. Nc,Ed: Axial compression applicant bad calculation = 9.976 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 270.00 cm2 · 2803.26 kp/cm2 = 756.881 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 2 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) If the slenderness ratio is λ≤0.2 or NC,Ed / Ncr ≤ 0.04 you can ignore the effect of buckling, and see only the cross section resistance. Where: N C , Ed 0 . 010 N Cr A· f y : Reduced slenderness = 0.87 N cr Ncr: Elastic critical elastic buckling. = 989.351 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): 51 a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 12503.995 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 989.351 t L kz c) Elastic critical axial buckling torque. 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: Iy: Moment of inertia of the gross section with the axis Y = 171000.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 13530.00 cm4 It: Moment of inertia of uniform torsion = 667.20 cm4 Iw: constant warping of the section = 10970000.00 cm6 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 Lky: effective length for buckling with the axis Y. =5.375 m Lkz: effective length for buckling with the axis Z. = 5.375 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 26.55 cm io (i y i z y 0 z 0 ) ( 25 ,17 7 . 08 0 0 ) 26 . 14 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 25.17 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.08 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 28 . 054 t ·m Ed 0 . 156 1 M c , Rd 180 . 110 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G +1.5·V1 (1). Where: MEd: Bending moment calculation applicant awful = 28.054 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 180.110 t·m 52 Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 6425.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 30 . 370 t ·m Ed 0 . 779 1 M c , Rd 38 . 993 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1(4). Where: MEd: Bending moment calculation applicant awful = 30.370 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 38.993 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1391.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 10 . 952 t 0 . 073 1 V c , Rd 150 . 517 t Where: VEd: Applicant for calculating shear badly. = 10.952 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 150.517 t 3 Where: Av: Cross-cutting area = h · tw = 93.00 cm2 h: Song of the section. = 600 mm tw: Web thickness. = 15.5 mm 53 Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 34.84 < 55.46 tw Where: d λw: Slenderness of the soul.= = 34.84 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 4 . 383 t 0 . 015 1 V c , Rd 301 . 520 t Where: VEd: Applicant for calculating shear badly. = 4.383 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 301.520t 3 Where: Av: Cross-cutting area = A - d · tw = 186.30 cm2 A: Gross sectional area.= 270.00 cm2 d: Web depth. = 540 mm tw: Web thickness. =15.5 mm 54 Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 9.630 ≤ 75.259 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(1). Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 4.383 ≤ 150.760 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(4). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.778 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.549 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.788 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(4). Where: Nc,Ed: Axil applicant compression calculation. = 3.999 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. 55 Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 2 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 180 . 110 tm M pl , Rd , y 180 . 110 tm 1 0 . 5·a na 2 na M N , Rd , z M pl , Rd , z ·1 =38.993 tm 1 a 2 5·n 0 . 025 1 N c , Ed n 0 . 005 N pl , Rd Npl,Rd: compressive strength of the gross section.= 756.881 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (180.110 tm and 38.993 tm) A 2·b·t f a 0 . 33 0 . 5 A A: Area of the gross section. = 270.00 cm2 b: width of the wing. = 30.00 cm tf: thickness of the wing = 30.00 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 108 tm 0 . 030 1 M T , Rd 3 . 599 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(4). MT,Ed: torque calculation applicant awful.= 0.108 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 3.599t m 3 Where: WT: Torsional modulus. = 222.40 cm3 56 Z shear resistance and torque combined (EN 1993-1-1 Eurocode 3: 2005) V Ed 0 . 834 t 0 . 006 1 V pl ,T , Rd 148 . 715 t Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05·N1. VEd: Applicant for calculating shear bad.= 0.834 t MT,Ed: Torque calculation applicant awful.= 0.107 t·m The shear resistance reduced calculation Vpl, T, Rd is given by: T , Ed V pl ,T , Rd 1 ·V pl , Rd 148 . 715 t f yd 1 . 25 · 3 Where: Vpl, Rd: Shear resistance of calculation = 150.517 t M T , Ed τT, Ed: Shear stresses due to torsion = 48 . 16 kN 2 Wt cm WT: Module torsional strength = 222.40 cm3 BEAM 4 200x200x18mm Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 17 . 367 t Must be satisfied: 0 . 049 1 N t , Rd 354 . 040 t The calculation effort lousy applicant occurs for the combination of actions 1.35·G+1.5·V1(3)+1.05N1. Nt,Ed: Axial traction applicant bad calculation = 17.367 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 126.30 cm2 · 2803.26 kp/cm2 = 354.040 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 57 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 17.652 t 0 . 050 1 N c , Rd 354.040 t N c , Ed 17.652 t 0 . 119 1 N b , Rd 147.853 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1(1). Nc,Ed: Axial compression applicant bad calculation = 17.652 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 126.30 cm2 · 2803.26 kp/cm2 = 354.040 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 1 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) The resistance of buckling Nb,Rd compressed in a bar is given by: Nb,Rd = χ ·A · fyd = 0.42·126.30 cm2 · 2803.26 kp/cm2 = 147.853 t Where: A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 χ: Reduction coefficient for buckling. 1 0.42 ≤ 1 ( ) 2 2 58 Where: 0 . 5· 1 · 0 . 2 ( ) 2 = 1.52 α: Reduction coefficient for buckling.= 0.49 A· f y : Reduced slenderness = 1.23 N cr Ncr: Elastic critical elastic buckling. = 232.293 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 232.293 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 232.293 t L kz Where: Iy: Moment of inertia of the gross section with the axis Y = 6818.49 cm4 Iz: moment of inertia of the gross section with the axis Z = 6818.49 cm4 E: Modulus of elasticity = 2140673 kp/cm2 Lky: effective length for buckling with the axis Y. = 7.875 m Lkz: effective length for buckling with the axis Z. = 7.875 m Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 16 . 139 t ·m Ed 0 . 642 1 M c , Rd 25 . 153 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G +1.5·V1 (4) +1.05·N1 Where: MEd: Bending moment calculation applicant awful = 16.139 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 25.153 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 59 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 897.26 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 2 . 732 t ·m Ed 0 . 109 1 M c , Rd 25 . 153 t ·m The calculation effort lousy applicant occurs for the combination of G + 1.5·V1(4). Where: MEd: Bending moment calculation applicant awful =2.732 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 25.153 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 897.26 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 8 . 206 t 0 . 086 1 V c , Rd 95 . 554 t Where: VEd: Applicant for calculating shear badly. = 8.206 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 95.554 t 3 Where: Av: Cross-cutting area = h · tw = 59.04 cm2 d: Song of the section. = 164 mm tw: Web thickness. = 18 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: 60 d 72 · 9.11 < 55.46 tw Where: d λw: Slenderness of the soul.= = 9.11 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 0 . 486 t 0 . 004 1 V c , Rd 108 . 851 t Where: VEd: Applicant for calculating shear badly. = 0.486 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 108.851 t 3 Where: Av: Cross-cutting area = A - d · tw = 67.26 cm2 A: Gross sectional area.= 126.30 cm2 d: Web depth. = 164 mm tw: Web thickness. = 18 mm Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. 61 V cRd V ED 7.233 ≤ 47.777 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+0.9·V1(3)+1.5·N1. Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 0.486 ≤ 54.426 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(4). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.499 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.755 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.532≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(4)+1.05·N1 Where: Nc,Ed: Axil applicant compression calculation. = 7.991 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively (16.139 t·m and 2.420 t·m). Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 62 1 n M N , Rd , y M pl , Rd 25 . 153 tm M pl , Rd , y 25 . 153 tm 1 0 . 5·a 1 n M N , Rd , z M pl , Rd , z =25.153 tm 1 0 . 5·a 1 . 661 1 . 66 1 . 661 6 1 1 . 13 ·n 2 N c , Ed n 0 . 023 N pl , Rd Npl,Rd: compressive strength of the gross section.=354.040 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively (25.153 t·m both). A 2·b·t f a 0 . 43 0 . 5 A A: Area of the gross section. = 126.30 cm2 b: width of the wing. = 20.00 cm h: ridge section = 200.00 cm tf: thickness of the wing = 18 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 098 tm 0 . 005 1 M T , Rd 19 . 259 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(3)+1.05·N1. MT,Ed: torque calculation applicant awful.= 0.098 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 19.259t m 3 Where: WT: Torsional modulus. = 1189.96 cm3 Z shear resistance and torque combined (EN 1993-1-1 Eurocode 3: 2005) V Ed 6 . 814 t 0 . 071 1 V pl ,T , Rd 95 . 383 t Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05·N1. 63 VEd: Applicant for calculating shear bad.= 6.814 t MT,Ed: Torque calculation applicant awful.= 0.034 t·m The shear resistance reduced calculation Vpl, T, Rd is given by: T , Ed V pl ,T , Rd 1 ·V pl , Rd 95 . 383 t f yd 1 . 25 · 3 Where: Vpl, Rd: Shear resistance of calculation = 95.554 t M T , Ed τT, Ed: Shear stresses due to torsion = 2 . 89 kN 2 Wt cm WT: Module torsional strength = 1192.46 cm3 BEAM 5 Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 3 . 368 t Must be satisfied: 0 . 004 1 N t , Rd 756 . 881 t The calculation effort lousy applicant occurs for the combination of actions 1.35·G+1.5·V1 (1)+1.05N1. Nt,Ed: Axial traction applicant bad calculation = 3.368 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 270.00 cm2 · 2803.26 kp/cm2 = 756.881 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 19.106 t 0 . 025 1 N c , Rd 756.881 t 64 The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (3). Nc,Ed: Axial compression applicant bad calculation = 19.106 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 270.00 cm2 · 2803.26 kp/cm2 = 756.881 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 2 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) If the slenderness ratio is λ≤0.2 or NC,Ed / Ncr ≤ 0.04 you can ignore the effect of buckling, and see only the cross section resistance. Where: N C , Ed 0 . 019 N Cr A· f y : Reduced slenderness = 0.87 N cr Ncr: Elastic critical elastic buckling. = 989.351 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): c) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 12503.995 t L ky d) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 989.351 t L kz e) Elastic critical axial buckling torque. 1 ·E ·I w 2 N cr ,T 2 · G ·I t 2 =∞ io L kt Where: 65 Iy: Moment of inertia of the gross section with the axis Y = 171000.00 cm4 Iz: moment of inertia of the gross section with the axis Z = 13530.00 cm4 It: Moment of inertia of uniform torsion = 667.20 cm4 Iw: constant warping of the section = 10970000.00 cm6 E: Modulus of elasticity = 2140673 kp/cm2 G: shear modulus = 825688 kp/cm2 Lky: effective length for buckling with the axis Y. =5.375 m Lkz: effective length for buckling with the axis Z. = 5.375 m Lkt: effective length for torsional buckling. = 0 m i0: polar turning radius of the gross section with respect to the torsion center = 26.55 cm io (i y i z y 0 z 0 ) ( 25 ,17 7 . 08 0 0 ) 26 . 14 cm 2 2 2 2 0 .5 2 2 0 .5 iy: radius of gyration of the gross section with respect to the principal axes of inertia Y = 25.17 cm iz: radius of gyration of the gross section with respect to the principal axes of inertia Z = 7.08 cm y0, z0: Coordinates of the center of torque in the direction of the principal axes Y and Z, respectively, relative to the center of gravity of the section = 0 cm. Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 35 . 579 t ·m Ed 0 . 198 1 M c , Rd 180 . 110 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G +1.5·V1 (1) +1.05·N1 Where: MEd: Bending moment calculation applicant awful = 35.579 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 180.110 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 6425.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: 66 M 29 . 491 t ·m Ed 0 . 756 1 M c , Rd 38 . 993 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1 (2). Where: MEd: Bending moment calculation applicant awful = 29.491 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 38.993 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 1391.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 13 . 751 t 0 . 091 1 V c , Rd 150 . 517 t Where: VEd: Applicant for calculating shear badly. = 13.751 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 150.517 t 3 Where: Av: Cross-cutting area = h · tw = 93.00 cm2 h: Song of the section. = 600 mm tw: Web thickness. = 15.5 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 34.84 < 55.46 tw Where: d λw: Slenderness of the soul.= = 34.84 tw 67 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 9 . 539 t 0 . 032 1 V c , Rd 301 . 520 t Where: VEd: Applicant for calculating shear badly. = 9.539 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 301.520t 3 Where: Av: Cross-cutting area = A - d · tw = 186.30 cm2 A: Gross sectional area.= 270.00 cm2 d: Web depth. = 540 mm tw: Web thickness. =15.5 mm Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 12.456 ≤ 75.259 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(1)+1.05·N1. 68 Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 9.539 ≤ 150.760 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(2). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.762 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.603 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.802 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions G+1.5·V1(2). Where: Nc,Ed: Axil applicant compression calculation. = 3.871 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively. Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 180 . 110 tm M pl , Rd , y 180 . 110 tm 1 0 . 5·a na 2 na M N , Rd , z M pl , Rd , z ·1 =38.993 tm 1 a 2 5·n 0 . 025 1 69 N c , Ed n 0 . 005 N pl , Rd Npl,Rd: compressive strength of the gross section.= 756.881 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (180.110 tm and 38.993 tm) A 2·b·t f a 0 . 33 0 . 5 A A: Area of the gross section. = 270.00 cm2 b: width of the wing. = 30.00 cm tf: thickness of the wing = 30.00 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 050 tm 0 . 014 1 M T , Rd 3 . 599 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(3). MT,Ed: torque calculation applicant awful.= 0.050 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 3.599t m 3 Where: WT: Torsional modulus. = 222.40 cm3 Z shear resistance and torque combined (EN 1993-1-1 Eurocode 3: 2005) V Ed 5 . 960 t 0 . 040 1 V pl ,T , Rd 150 . 480 t Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05·N1. VEd: Applicant for calculating shear bad.= 5.960 t MT,Ed: Torque calculation applicant awful.= 0.001 t·m The shear resistance reduced calculation Vpl, T, Rd is given by: T , Ed V pl ,T , Rd 1 ·V pl , Rd 150 . 480 t f yd 1 . 25 · 3 70 Where: Vpl, Rd: Shear resistance of calculation = 150.517 t M T , Ed τT, Ed: Shear stresses due to torsion = 1 . 01 kN 2 Wt cm WT: Module torsional strength = 222.40 cm3 71 CROSSES CROSS 1 D=180mm t=18mm Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 24 . 445 t Must be satisfied: 0 . 095 1 N t , Rd 256 . 804 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (1). Nt,Ed: Axial traction applicant bad calculation = 24.445 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 91.61 cm2 · 2803.26 kp/cm2 = 256.804 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 72 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 32.279 t 0 . 126 1 N c , Rd 256.804 t N c , Ed 32.279 t 0 . 365 1 N b , Rd 88.337 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1 (3) +1.05·N1. Nc,Ed: Axial compression applicant bad calculation = 32.279 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 91.61 cm2 · 2803.26 kp/cm2 = 256.804 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 1 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) The resistance of buckling Nb,Rd compressed in a bar is given by: Nb,Rd = χ ·A · fyd = 0.34· 91.61 cm2 · 2803.26 kp/cm2 = 88.337 t Where: A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 χ: Reduction coefficient for buckling. 1 0.34 ≤ 1 ( ) 2 2 Where: 73 0 . 5· 1 · 0 . 2 ( ) 2 = 1.80 α: Reduction coefficient for buckling.= 0.49 A· f y : Reduced slenderness = 1.41 N cr Ncr: Elastic critical elastic buckling. = 128.394 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 128.394 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 128.394 t L kz Where: Iy: Moment of inertia of the gross section with the axis Y = 3042.33 cm4 Iz: moment of inertia of the gross section with the axis Z = 3042.33 cm4 E: Modulus of elasticity = 2140673 kp/cm2 Lky: effective length for buckling with the axis Y. = 7.075 m Lkz: effective length for buckling with the axis Z. = 7.075 m Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 0 . 288 t ·m Ed 0 . 022 1 M c , Rd 1 3 . 297 t ·m The calculation effort lousy applicant occurs for the combination of 1.35G +1.5·V1(1) Where: MEd: Bending moment calculation applicant awful = 0.288 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 13.297 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 474.34 cm3 74 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 9 . 471 t ·m Ed 0 . 712 1 M c , Rd 13 . 297 t ·m The calculation effort lousy applicant occurs for the combination of G+1.5·V1(4). Where: MEd: Bending moment calculation applicant awful = 9.471 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 13.297 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 474.34 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 0 . 191 t 0 . 002 1 V c , Rd 94 . 389 t Where: VEd: Applicant for calculating shear badly. = 0.191 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 94.389 t 3 Where: A Av: Cross-cutting area = 2· = 58.32 cm2 A: Area of the section. = 91.61 cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 3 . 581 t 0 . 038 1 V c , Rd 94 . 389 t Where: 75 VEd: Applicant for calculating shear badly. = 3.581 t The shear resistance of calculating VcRd is given by: f yd VCRd = A v 94.389 t 3 Where: A Av: Cross-cutting area = 2· = 58.32 cm2 A: Area of the section. = 91.61 cm2 Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 0.191 ≤ 47.194 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(3)+1.05N1. Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 3.581 ≤ 47.194 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(4). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.503 ≤ 1 M N , Rd , y M N , Rd , z 76 N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.474 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.758≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(4)+1.05N1. Where: Nc,Ed: Axil applicant compression calculation. = 3.283 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively (0.222 t·m and 9.426 t·m). Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 . 04 ·M (1 n ) 13 . 297 tm M 13 . 297 .tm 1 .7 M N , Rd , y pl , Rd , y pl , Rd , y 1 . 04 ·M (1 n ) 13 . 297 tm M 13 . 297 .tm 1 .7 M N , Rd , z pl , Rd , z pl , Rd , z 2 5·n 2 1 N c , Ed n 0 . 013 N pl , Rd Npl,Rd: compressive strength of the gross section.= 256.804 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (13.297 tm both) Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 671 tm 0 . 061 1 M T , Rd 19 . 942 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(4). MT,Ed: torque calculation applicant awful.= 0.671 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 19.942 t m 3 77 Where: WT: Torsional modulus. = 676.07 cm3 CROSS 2 D=350mm t=30mm Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 46 . 150 t Must be satisfied: 0 . 055 1 N t , Rd 845 . 444 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1(1). Nt,Ed: Axial traction applicant bad calculation = 46.150 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 301.59 cm2 · 2803.26 kp/cm2 = 845.444 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 65.228 t 0 . 077 1 N c , Rd 845.444 t The calculation effort lousy applicant occurs for the combination of actions 1.35·G+1.5·V1 (3)+1.05N1. Nc,Ed: Axial compression applicant bad calculation = 65.228 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 301.59 cm2 · 2803.26 kp/cm2 = 845.444 t Where: 78 Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 1 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) If the slenderness ratio is λ≤0.2 or NC,Ed / Ncr ≤ 0.04 you can ignore the effect of buckling, and see only the cross section resistance. Where: N C , Ed 0 . 034 N Cr A: Area of the gross section of Class 1, 2 and 3 = 301.59 cm2. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 A· f y : Reduced slenderness = 0.67 N cr Ncr: Elastic critical elastic buckling. = 1903.546 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 1903.546 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 1903.546 t L kz Where: Iy: Moment of inertia of the gross section with the axis Y = 38943.18 cm4 Iz: moment of inertia of the gross section with the axis Z = 38943.18 cm4 E: Modulus of elasticity = 2140673 kp/cm2 Lky: effective length for buckling with the axis Y. = 6.574 m Lkz: effective length for buckling with the axis Z. = 6.574 m 79 Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 3 . 374 t ·m Ed 0 . 039 1 M c , Rd 86 . 369 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G + 1.5·V1 (1). Where: MEd: Bending moment calculation applicant awful = 3.374 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 86.369 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 3081.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 31 . 101 t ·m Ed 0 . 360 1 M c , Rd 86 . 369 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1(2). Where: MEd: Bending moment calculation applicant awful = 31.101 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 86.369 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 3081.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 0 . 972 t 0 . 003 1 V c , Rd 310 . 745 t 80 Where: VEd: Applicant for calculating shear badly. = 0.972 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 310.745 t 3 Where: A Av: Cross-cutting area = 2· = 192.00 cm2 A: Area of the section. = 301.59 cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 6 . 899 t 0 . 022 1 V c , Rd 310 . 745 t Where: VEd: Applicant for calculating shear badly. = 2.050 t The shear resistance of calculating V cRd is given by: f yd VCRd = A v 262.191 t 3 Where: A Av: Cross-cutting area = 2· = 192.00 cm2 A: Area of the section. = 301.59 cm2 Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 0.915 ≤ 155.373 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(3)+1.05·N1. 81 Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 6.899 ≤ 155.373 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(2). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.130 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.233 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N t , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.375≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(2). Where: Nc,Ed: Axil applicant traction calculation. = 9.175 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively (0.479 t·m and 31.089 t·m). Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. (1 n ) M N , Rd , y M pl , Rd , y 86 . 369 tm M pl , Rd , y 86 . 369 .tm 1 0 . 5·a w (1 n ) M N , Rd , z M pl , Rd , z 86 . 369 tm M pl , Rd , z 86 . 369 .tm 1 0 . 5·a f 2 Where: 82 N t , Ed n= 0 . 011 N pl , Rd Npl,Rd: compressive strength of the gross section.= 845.444 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (86.369 tm both) Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 7 . 303 tm 0 . 101 1 M T , Rd 72 . 032 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(2). MT,Ed: torque calculation applicant awful.= 7.303 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 72.032 t m 3 Where: WT: Torsional modulus. = 4450.65 cm3 CROSS 3 D=180mm t=18mm Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 12 . 029 t Must be satisfied: 0 . 047 1 N t , Rd 256 . 804 t The calculation effort lousy applicant occurs for the combination of actions 1.35G+1.5·V1(1). Nt,Ed: Axial traction applicant bad calculation = 12.029 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 91.61 cm2 · 2803.26 kp/cm2 = 256.804 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. 83 fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 30.510 t 0 . 119 1 N c , Rd 256.804 t N c , Ed 30.510 t 0 . 316 1 N b , Rd 96.600 t The calculation effort lousy applicant occurs for the combination of actions G+ +1.5·V1 (3) +1.05·N1. Nc,Ed: Axial compression applicant bad calculation = 32.279 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 91.61 cm2 · 2803.26 kp/cm2 = 256.804 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 1 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) The resistance of buckling Nb,Rd compressed in a bar is given by: Nb,Rd = χ ·A · fyd = 0.38· 91.61 cm2 · 2803.26 kp/cm2 = 86.600 t Where: A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 χ: Reduction coefficient for buckling. 84 1 0.38 ≤ 1 ( ) 2 2 Where: 0 . 5· 1 · 0 . 2 ( ) 2 = 1.66 α: Reduction coefficient for buckling.= 0.49 A· f y : Reduced slenderness = 1.33 N cr Ncr: Elastic critical elastic buckling. = 145.054 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 145.054 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 145.054 t L kz Where: Iy: Moment of inertia of the gross section with the axis Y = 3042.33 cm4 Iz: moment of inertia of the gross section with the axis Z = 3042.33 cm4 E: Modulus of elasticity = 2140673 kp/cm2 Lky: effective length for buckling with the axis Y. = 6.657 m Lkz: effective length for buckling with the axis Z. = 6.657m Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 0 . 370 t ·m Ed 0 . 028 1 M c , Rd 1 3 . 297 t ·m The calculation effort lousy applicant occurs for the combination of 1.35G +1.5·V1(3) Where: MEd: Bending moment calculation applicant awful = 0.370 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 13.297 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 85 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 474.34 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 5 . 301 t ·m Ed 0 . 399 1 M c , Rd 13 . 297 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G+ 1.5·V1(2)+1.05·N1. Where: MEd: Bending moment calculation applicant awful = 5.301 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 13.297 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 474.34 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 0 . 210 t 0 . 002 1 V c , Rd 94 . 389 t Where: VEd: Applicant for calculating shear badly. = 0.210t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 94.389 t 3 Where: A Av: Cross-cutting area = 2· = 58.32 cm2 A: Area of the section. = 91.61 cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied:: 86 V Ed 3 . 052 t 0 . 032 1 V c , Rd 94 . 389 t Where: VEd: Applicant for calculating shear badly. = 3.052 t The shear resistance of calculating VcRd is given by: f yd VCRd = A v 94.389 t 3 Where: A Av: Cross-cutting area = 2· = 58.32 cm2 A: Area of the section. = 91.61 cm2 Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 0.199 ≤ 47.194 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(1)+1.05N1. Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 0.155 ≤ 47.194 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(3). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: 87 M y , Ed M z , Ed 1 0.157 ≤ 1 M N , Rd , y M N , Rd , z N t , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.416 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.416≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(2). Where: Nt,Ed: Axil applicant traccion calculation. = 1.246 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively (0.203 t·m and 5.261 t·m). Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 . 04 ·M (1 n ) 13 . 297 tm M 13 . 297 .tm 1 .7 M N , Rd , y pl , Rd , y pl , Rd , y 1 . 04 ·M (1 n ) 13 . 297 tm M 13 . 297 .tm 1 .7 M N , Rd , z pl , Rd , z pl , Rd , z 2 1 . 66 26 1 1 . 13 n 2 N c , Ed n 0 . 005 N pl , Rd Npl,Rd: compressive strength of the gross section.= 256.804 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (13.297 tm both) Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 0 . 369 tm 0 . 034 1 M T , Rd 10 . 942 tm Applicants efforts produced dismal spreadsheet for the combination of 1.35·G +1.5·V1(3)+1.05N1. MT,Ed: torque calculation applicant awful.= 0.369 t m 88 The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 10.942 t m 3 Where: WT: Torsional modulus. = 676.07 cm3 CROSS 4 200x200x18mm Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 22 . 148 t Must be satisfied: 0 . 063 1 N t , Rd 354 . 040 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1(1). Nt,Ed: Axial traction applicant bad calculation = 22.148 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 126.30 cm2 · 2803.26 kp/cm2 = 354.040 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 20.757 t 0 . 059 1 N c , Rd 354.040 t The calculation effort lousy applicant occurs for the combination of actions 1.35G +1.5·V1(3)+1.05N1. Nc,Ed: Axial compression applicant bad calculation = 20.757 t The compressive strength calculation Nc,Rd is given by: 89 Nc,Rd = A · fyd = 126.30 cm2 · 2803.26 kp/cm2 = 354.040 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 1 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) If the slenderness ratio is λ≤0.2 or NC,Ed / Ncr ≤ 0.04 you can ignore the effect of buckling, and see only the cross section resistance. Where: N C , Ed 0 . 033 N Cr A· f y : Reduced slenderness = 0.75 N cr Ncr: Elastic critical elastic buckling. = 633.857 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 633.857 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 633.857 t L kz Where: Iy: Moment of inertia of the gross section with the axis Y = 6818.49 cm4 Iz: moment of inertia of the gross section with the axis Z = 6818.49 cm4 E: Modulus of elasticity = 2140673 kp/cm2 Lky: effective length for buckling with the axis Y. = 4.767 m Lkz: effective length for buckling with the axis Z. = 4.767 m 90 Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 18 . 818 t ·m Ed 0 . 470 1 M c , Rd 25 . 153 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G +1.5·V1 (4) +1.05·N1 Where: MEd: Bending moment calculation applicant awful = 11.818 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 25.153 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 897.26 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 4 . 207 t ·m Ed 0 . 167 1 M c , Rd 25 . 153 t ·m The calculation effort lousy applicant occurs for the combination of G + 1.5·V1(4). Where: MEd: Bending moment calculation applicant awful =2.732 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 25.153 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 897.26 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: 91 V Ed 4 . 243 t 0 . 044 1 V c , Rd 95 . 554 t Where: VEd: Applicant for calculating shear badly. = 4.243 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 95.554 t 3 Where: Av: Cross-cutting area = h · tw = 59.04 cm2 d: Song of the section. = 164 mm tw: Web thickness. = 18 mm Shear buckling of the soul (EN 1993-1-1 Eurocode 3) Although no transverse stiffeners are arranged, it is not necessary to check the buckling resistance of the soul, since it satisfies: d 72 · 11.11 < 55.46 tw Where: d λw: Slenderness of the soul.= = 11.11 tw 72 λmax: Maximum slenderness = · =55.46 ƞ: coefficient to consider the additional resistance due to plastic regime hardening of the material.= 1.20 f ref ɛ: Reduction factor = = 0.92 fy fref: Reference Yield.= 2395.51 kp/cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied: V Ed 1 . 166 t 0 . 011 1 V c , Rd 108 . 851 t Where: VEd: Applicant for calculating shear badly. = 1.166 t 92 The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 108.851 t 3 Where: Av: Cross-cutting area = A - d · tw = 67.26 cm2 A: Gross sectional area.= 126.30 cm2 d: Web depth. = 164 mm tw: Web thickness. = 18 mm Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 4.243 ≤ 47.777 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05·N1. Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 1.166 ≤ 54.426 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(4). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.326 ≤ 1 M N , Rd , y M N , Rd , z 93 N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.621 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N c , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.491≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(4)+1.05·N1 Where: Nc,Ed: Axil applicant compression calculation. = 17.648 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively (11.818 t·m and 3.714 t·m). Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 1 n M N , Rd , y M pl , Rd 25 . 153 tm M pl , Rd , y 25 . 153 tm 1 0 . 5·a 1 n M N , Rd , z M pl , Rd , z =25.153 tm 1 0 . 5·a 1 . 665 1 . 66 1 . 665 6 1 1 . 13 ·n 2 N c , Ed n 0 . 050 N pl , Rd Npl,Rd: compressive strength of the gross section.=354.040 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively (25.153 t·m both). A 2·b·t f a 0 . 43 0 . 5 A A: Area of the gross section. = 126.30 cm2 b: width of the wing. = 20.00 cm h: ridge section = 200.00 cm tf: thickness of the wing = 18 mm Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: 94 M T , Ed 0 . 098 tm 0 . 069 1 M T , Rd 19 . 259 tm Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(4)+1.05·N1. MT,Ed: torque calculation applicant awful.= 1.334 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 19.259t m 3 Where: WT: Torsional modulus. = 1189.96 cm3 CROSS 5 D=350mm t=30mm Tensile (Eurocode 3 EN 1993-1-1): N t , Ed 15 . 033 t Must be satisfied: 0 . 018 1 N t , Rd 845 . 444 t The calculation effort lousy applicant occurs for the combination of actions G+1.5·V1(4). Nt,Ed: Axial traction applicant bad calculation = 15.033 t The tensile strength Nt,Rd is: Nt,Rd= A·fyd = 301.59 cm2 · 2803.26 kp/cm2 = 845.444 t Where: A: Gross area of the cross section of the bar. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Compressive strength (EN 1993-1-1 Eurocode 3) Must be satisfied: N c , Ed 35.103 t 0 . 042 1 N c , Rd 845.444 t 95 The calculation effort lousy applicant occurs for the combination of actions 1.35·G+1.5·V1(2)+1.05N1. Nc,Ed: Axial compression applicant bad calculation = 35.103 t The compressive strength calculation Nc,Rd is given by: Nc,Rd = A · fyd = 301.59 cm2 · 2803.26 kp/cm2 = 845.444 t Where: Class: Class section, as the deformation capacity and development of the plastic resistance of compressed flat elements of a section = 1 A: Area of the gross section to the sections of Class 1, 2 and 3. fyd: Resistance of the steel. fyd = fy / ɣMo =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣMo: Partial safety of the material = 1.00 Buckling resistance (EN 1993-1-1 Eurocode 3) If the slenderness ratio is λ≤0.2 or NC,Ed / Ncr ≤ 0.04 you can ignore the effect of buckling, and see only the cross section resistance. Where: N C , Ed 0 . 020 N Cr A: Area of the gross section of Class 1, 2 and 3 = 301.59 cm2. fyd: Resistance of the steel. fyd = fy / ɣM1 =2803.26 kp/cm2 fy: Elastic limit = 2803.26 kp/cm2 ɣM1: Partial safety of the material = 1.00 A· f y : Reduced slenderness = 0.69 N cr Ncr: Elastic critical elastic buckling. = 1798.263 t The elastic critical elastic buckling Ncr is the smaller of the values obtained in a), b) and c): a) Axil elastic critical for buckling about the axis Y. ·E ·I y 2 N cr , y 2 1798.263 t L ky b) Elastic critical buckling elastic bending about the Z axis · E ·I z 2 N cr , z 2 = 1798.26 t L kz 96 Where: Iy: Moment of inertia of the gross section with the axis Y = 38943.18 cm4 Iz: moment of inertia of the gross section with the axis Z = 38943.18 cm4 E: Modulus of elasticity = 2140673 kp/cm2 Lky: effective length for buckling with the axis Y. = 6.764 m Lkz: effective length for buckling with the axis Z. = 6.764 m Flexural axis Y (EN 1993-1-1 Eurocode 3) Must be satisfied: M 1 . 725 t ·m Ed 0 . 020 1 M c , Rd 86 . 369 t ·m The calculation effort lousy applicant occurs for the combination of 1.35·G + 1.5·V1 (4)+1.05N1. Where: MEd: Bending moment calculation applicant awful = 1.7254 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,y · fyd = 86.369 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 Wpl,y : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 3081.00 cm3 Flexural axis Z (EN 1993-1-1 Eurocode 3) Must be satisfied: M 21 . 903 t ·m Ed 0 . 254 1 M c , Rd 86 . 369 t ·m The calculation effort lousy applicant occurs for the combination of G +1.5·V1(1). Where: MEd: Bending moment calculation applicant awful = 21.903 t·m The bending moment resistance calculation Mc,Rd is given by: Mc,Rd= W pl,z · fyd = 86.369 t·m Where: Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements of a simple bending section. = 1 97 Wpl,z : Plastic modulus for the fiber with higher voltage, for sections 1 and 2 class.= 3081.00 cm3 Shear strength Z (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 0 . 924 t 0 . 003 1 V c , Rd 310 . 745 t Where: VEd: Applicant for calculating shear badly. = 0.924 t The shear resistance of calculating V cRd is given by: f yd Vc,Rd = A v 310.745 t 3 Where: A Av: Cross-cutting area = 2· = 192.00 cm2 A: Area of the section. = 301.59 cm2 Shear strength Y (EN 1993-1-1 Eurocode 3) Must be satisfied:: V Ed 7 . 845 t 0 . 025 1 V c , Rd 310 . 745 t Where: VEd: Applicant for calculating shear badly. = 7.845 t The shear resistance of calculating VcRd is given by: f yd VCRd = A v 262.191 t 3 Where: A Av: Cross-cutting area = 2· = 192.00 cm2 A: Area of the section. = 301.59 cm2 Resistance to bending moment Y and Z combined shear (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. 98 V cRd V ED 0.805 ≤ 155.373 2 Applicants efforts produced dismal spreadsheet for the combination of 1.35·G+1.5·V1(2)+1.05·N1. Resistance to bending moment (Z) and shear (Y) combined (EN 1993-1-1 Eurocode 3) It is not necessary to reduce the design moment resistance, as the applicant for calculating shear bad VED does not exceed 50% of the design shear strength VcRd. V cRd V ED 7.845 ≤ 155.373 2 Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(1). Resistance to bending and combined axial (EN 1993-1-1 Eurocode 3) Must be satisfied: M y , Ed M z , Ed 1 0.062 ≤ 1 M N , Rd , y M N , Rd , z N c , Ed M M z , Ed y ,Ed k yy · k yz · 1 0.172 ≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd N t , Ed M M z , Ed y ,Ed k zy · k zz · 1 0.272≤ 1 y · A· f yd LT ·W pl , y · f yd W pl , z · f yd Applicants efforts produced dismal spreadsheet for the combination of actions 1.35·G+1.5·V1(1)+1.05N1. Where: Nc,Ed: Axil applicant traction calculation. = 17.308 t m My, Ed, Mz, Ed: Applicants for calculating bending moments dismal, according to the axes Y and Z, respectively (0.155 t·m and 21.530 t·m). Class: Class of the section as the deformation capacity and development of the plastic resistance of flat elements, for axial and bending simple. = 1 MN, Rd,y and MN, Rd, z: small plastic bending moment resistance calculation, about Y and Z axes, respectively. 99 (1 n ) M N , Rd , y M pl , Rd , y 86 . 369 tm M pl , Rd , y 86 . 369 .tm 1 0 . 5·a w (1 n ) M N , Rd , z M pl , Rd , z 86 . 369 tm M pl , Rd , z 86 . 369 .tm 1 0 . 5·a f 2 Where: N t , Ed n= 0 . 020 N pl , Rd Npl,Rd: compressive strength of the gross section.= 845.444 t Mpl,Rd,y , Mpl,Rd,z: Flexural strength of the gross section plastic conditions with respect to Y and Z axes, respectively. (86.369 tm both) Torsional strength (EN 1993-1-1 Eurocode 3: 2005) Must be satisfied: M T , Ed 7 . 783 tm 0 . 108 1 M T , Rd 72 . 032 tm Applicants efforts produced dismal spreadsheet for the combination of G+1.5·V1(2). MT,Ed: torque calculation applicant awful.= 7.783 t m The resistant torque calculation MT,Rd is given by: 1 M T , Rd ·W T · f yd 72.032 t m 3 Where: WT: Torsional modulus. = 4450.65 cm3 100 ANNEX B: Plans of portics and joints ANNEX C: Checkings of Joints In this file, we will check all the joints of the portics, the tall and the short one. We have used the Eurocode 3 to determinate the number of bolts, the lenght of the weldings, the dimensions of the joint... All the joints are showed like a croquis in the Annex B. J1 8 ,9 f yo t 0 b1 b 2 2 1 kn 0 ,5 N i , Rd sin( i ) 2 b o M 5 b0 150 7 ,5 2 t0 2 10 b1 h1 b 2 h 2 120 120 120 120 0 ,8 4b0 4·150 161 ,83 kN 42 , 07 10 mm 2 2 0 , Ed 3 275 10 kN k n 1( tension ) f yo mm 2 n 0 ,1398 0 , 4·n 0 , 4 0 ,1398 M5 1 k 1,3 1,3 1, 23 1( comp ) n 0 ,8 8 , 9 275 N 10 2 mm 2 120 120 1 1 57 º N 1 , Rd 2 150 7 ,5 1 1 639 ,37 kN 0 ,5 sin( 57 º ) 8 ,9 275 N 10 2 mm 2 120 120 1 1 53 º N 2 , Rd 2 150 7 , 5 1 1 671 , 42 kN 0 ,5 sin( 53 º ) 0 ,55 ·h o e 0 , 25 ·ho 0 ,55 ·150 37 0 , 25 ·150 82 ,5 37 37 ,5 b1 / 2 120 0 ,8 0 ,35 b0 150 b1 / 2 210000 N 2 120 E mm 12 1, 25 · 1, 25 34 ,54 t1 / 2 10 f y1 275 N 2 mm b1 / 2 b0 120 150 0 ,1 0 , 01 0 ,1 0 , 01 0 ,8 0 , 25 b0 t0 150 10 b1 / 2 120 12 35 t1 / 2 10 b0 150 15 15 35 t0 10 b1 b 2 120 120 0 ,6 1,3 0 , 6 1,3 0 , 6 1 1,3 2 b1 2·120 g 20 t 1 t 2 10 10 20 b1 h1 b 2 h 2 120 120 120 120 0 ,8 4b0 4·150 g 20 1,5·1 1,5·1 0 ,8 0 ,13 0 ,3 b0 150 g 20 0 ,5·1 0 ,5·1 0 ,8 0 ,13 0 ,1 b0 150 275 N 2·10 10 f yo ·t 0 10 mm b eff · ·b i · ·120 80 mm b 0 f y 1 ·t i 150 275 N 2·10 mm t0 10 J2 8 , 9 f yo t 0 b1 b 2 2 1 kn 0 ,5 N i , Rd sin( i ) 2 b o M 5 b0 150 7 ,5 2 t0 2 10 b1 h1 b 2 h 2 120 120 100 100 0 , 73 4b0 4·150 105 , 04 kN 42 , 07 10 mm 2 2 0 , Ed 275 10 3 kN k n 1( tension ) f yo mm 2 n1 0 , 0911 0 , 4·n 0 , 4 0 , 0911 M5 1 k 1, 3 1, 3 1, 254 1( comp ) n 0 ,8 105 , 04 kN 34 , 07 10 mm 2 2 0 , Ed 275 10 3 kN k n 1( tension ) f yo mm 2 n2 0 ,1398 0 , 4·n 0 , 4 0 ,1398 M5 1 k n 1, 3 1, 3 1, 23 1( comp ) 0 ,8 8 , 9 275 N 10 2 mm 2 120 100 1 1 2 55 º N 1 , Rd 2 150 7 , 5 1 1 600 , 05 kN 0 ,5 sin( 55 º ) 0 ,55 ·h o e 0 , 25 ·ho 0 ,55 ·150 37 ,5 0 , 25 ·150 82 ,5 37 ,5 37 ,5 b1 120 0 ,8 0 , 35 b0 150 b2 100 0 , 66 0 , 35 b0 150 b1 210000 N 2 120 E mm 12 1, 25 · 1, 25 34 ,54 t1 10 f y1 275 N 2 mm b2 210000 N 2 100 E mm 10 1, 25 · 1, 25 34 ,54 t2 10 f y1 275 N 2 mm b1 b0 120 150 0 ,1 0 , 01 0 ,1 0 , 01 0 ,8 0 , 25 b0 t0 150 10 b2 b0 100 150 0 ,1 0 , 01 0 ,1 0 , 01 0 , 66 0 , 25 b0 t0 150 10 b1 120 20 35 t1 10 b2 100 10 35 t2 10 b0 150 15 15 35 t0 10 b1 b 2 120 100 0 ,6 1,3 0 , 6 1,3 0 , 6 0 ,916 1,3 2 b1 2·120 g 25 t 1 t 2 10 10 20 g 25 1,5·1 1,5·1 0 , 73 0 ,166 0 , 4 b0 150 g 25 0 ,5·1 0 ,5·1 0 , 73 0 ,166 0 ,135 b0 150 275 N 2· 10 10 f yo ·t 0 10 mm b eff · ·b1 · ·120 80 mm b 0 f y 1 ·t 1 150 275 N ·10 2 mm t0 10 275 N 2· 10 10 f yo ·t 0 10 mm b eff · ·b 2 · ·100 66 , 67 mm b 0 f y 1 ·t 2 150 275 N ·10 2 mm t0 10 J3 8 ,9 f yo t 0 b 1 b 2 2 1 N i , Rd kn 0 ,5 sin( i ) 2 b o M 5 b0 150 7 ,5 2 t0 2 10 b1 h1 b 2 h 2 100 100 100 100 0 , 6667 4b 0 4·150 54 , 77 kN 34 , 07 10 mm 2 2 0 , Ed 275 10 3 kN k n 1( tension ) f yo mm 2 n1 0 , 0585 0 , 4·n 0 , 4 0 , 0911 1 k n 1,3 1,3 1, 27 1( comp ) M 5 0 ,8 8 ,9 275 N 10 2 mm 2 100 100 1 1 2 55 º N 1 , Rd 2 150 7 ,5 1 1 545 ,503 kN 0 ,5 sin( 55 º ) 0 ,55 ·h o e 0 , 25 ·ho 0 ,55 ·150 37 ,5 0 , 25 ·150 82 ,5 37 ,5 37 ,5 b1 / 2 100 0 , 66 0 , 35 b0 150 b1 / 2 210000 N 2 100 E mm 10 1, 25 · 1, 25 34 ,54 t1 / 2 10 f y1 275 N 2 mm b1 / 2 b0 100 150 0 ,1 0 , 01 0 ,1 0 , 01 0 , 66 0 , 25 b0 t0 150 10 b1 / 2 100 10 35 t1 / 2 10 b0 150 15 15 35 t0 10 b1 b 2 100 100 0 ,6 1,3 0 , 6 1,3 0 , 6 1 1,3 2 b1 2·100 g 37 t 1 t 2 10 10 20 g 37 1,5·1 1,5·1 0 , 66 0 , 246 0 , 495 b0 150 g 37 0 ,5·1 0 ,5·1 0 , 66 0 , 246 0 ,165 b0 150 275 N 2· 10 10 f yo ·t 0 10 mm b eff · ·b i · ·100 66 , 67 mm b 0 f y 1 ·t i 150 275 N ·10 2 mm t0 10 J4 Strength to endure: 35,329t = 346,46kN Kind of Bolts: 8.8(fy=800N/mm2 and M20(As=245mm2 ; d=20mm; d0=22mm) 0 , 6· f y · A s 0 , 6·800 ·245 F v , Rd 94 ,1kN 1, 25 1, 25 346 ,36 kN Number of bolts = 3, 68 bolts 4 bolts 94 ,1kN / bolt e 1 1, 2·d 0 26 , 4 mm e 2 1, 5·d 0 33 mm p 1 2 , 2·d 0 48 , 4 mm p 2 3 , 0·d 0 66 mm Also, we have to check the welding that is between the hollow profile and the small plate in each side. fu 3 f v ,Wd w M 2 fu tensile strength of steel plates welded γM2 = 1.25 partial safety factor of the welded joint βW correlation coefficient depending on the type of steel parts soldiers The throat thickness of fillet weld must be such that: a 0 , 7 e min a 0 , 7 10 mm a 7 mm We have taken a= 5mm. The length of the weld will be: F Ed Lw 2 a f v ,Wd 346 , 46 10 N 3 Lw 2 5 mm 222 , 7 N 2 mm L w 155 ,57 mm J5 Strength to endure: 50,195t = 492,24kN Kind of Bolts: 8.8(fy=800N/mm2 and M24(As=353mm2 ; d=24mm; d0=26mm) 0 , 6· f y · A s 0 , 6·800 ·353 F v , Rd 135 , 6 kN 1, 25 1, 25 492 , 24 kN Number of bolts = 3, 63 bolts 4 bolts 135 , 6 kN / bolt e 1 1, 2·d 0 31 , 2 mm e 2 1, 5·d 0 39 mm p 1 2 , 2·d 0 57 , 2 mm p 2 3 , 0·d 0 78 mm Also, we have to check the welding that is between the hollow profile and the small plate in each side. fu 3 f v ,Wd w M 2 fu tensile strength of steel plates welded γM2 = 1.25 partial safety factor of the welded joint βW correlation coefficient depending on the type of steel parts soldiers The throat thickness of fillet weld must be such that: a 0 , 7 e min a 0 , 7 10 mm a 7 mm We have taken a= 5mm. The length of the weld will be: F Ed Lw 2 a f v ,Wd 492 , 24 10 N 3 Lw 2 5 mm 222 , 7 N 2 mm L w 221 , 03 mm J6 8 ,9 f yo t 0 b1 b 2 2 1 kn 0 ,5 N i , Rd sin( i ) 2 b o M 5 b0 200 8 . 33 2 t0 2 12 b1 h1 b 2 h 2 140 140 140 140 0 ,7 4b0 4·200 311 , 74 kN 50 , 07 10 mm 2 2 0 , Ed 3 275 10 kN k n 1( tension ) f yo mm 2 n1 0 , 2264 0 , 4·n 0 , 4 0 , 2264 M5 1 k 1,3 1,3 1,171 1( comp ) n 0 ,7 8 ,9 275 N 10 2 mm 2 140 140 1 1 2 53 º N 1, Rd 2 200 8 ,33 1 1 619 ,148 kN 0 ,5 sin( 53 º ) 0 ,55 ·h o e 0 , 25 ·ho 0 ,55 ·200 30 0 , 25 ·200 110 30 50 b1 / 2 140 0 , 7 0 ,35 b0 200 b1 / 2 210000 N 2 140 E mm 14 1, 25 · 1, 25 34 ,54 t1 / 2 10 f y1 275 N 2 mm b1 / 2 b0 140 200 0 ,1 0 , 01 0 ,1 0 , 01 0 , 7 0 , 26 b0 t0 200 12 b1 / 2 140 14 35 t1 / 2 10 b0 200 15 16 , 667 35 t0 12 b1 b 2 140 140 0 ,6 1,3 0 , 6 1,3 0 , 6 1 1,3 2 b1 2·140 g 22 t 1 t 2 10 10 20 g 22 1,5·1 1,5·1 0 , 7 0 ,15 0 , 45 b0 200 g 22 0 ,5·1 0 ,5·1 0 , 7 0 ,15 0 ,15 b0 200 275 N 2· 12 10 f yo ·t 0 10 mm b eff · ·b i · ·140 100 ,8 mm b 0 f y 1 ·t i 200 275 N ·10 2 mm t0 12 J7 8 , 9 f yo t 0 b1 b 2 2 1 kn 0 ,5 N i , Rd sin( i ) 2 b o M 5 b0 200 8 . 33 2 t0 2 12 b1 h1 b 2 h 2 140 140 120 120 0 , 65 4b0 4·200 304 ,95 kN 50 , 07 10 mm 2 2 0 , Ed 3 275 10 kN k n 1( tension ) f yo mm 2 n1 0 , 2215 0 , 4·n 0 , 4 0 , 2215 M5 1 k 1,3 1,3 1,163 1( comp ) n 0 , 65 190 , 27 kN 42 , 07 10 mm 2 2 0 , Ed 3 275 10 kN k n 1( tension ) f yo mm 2 n1 0 ,164 0 , 4·n 0 , 4 0 ,164 M5 1 k n 1,3 1, 3 1,198 1( comp ) 0 , 65 8 ,9 275 N 10 2 mm 2 140 120 1 1 2 53 º N 1 , Rd 2 200 8 ,33 1 1 353 , 798 kN 0 ,5 sin( 53 º ) 0 ,55 ·h o e 0 , 25 ·ho 0 ,55 ·200 30 0 , 25 ·200 110 30 50 b1 140 0 , 7 0 , 35 b0 200 b2 120 0 , 6 0 , 35 b0 200 b1 210000 N 2 140 E mm 14 1, 25 · 1, 25 34 ,54 t1 10 f y1 275 N 2 mm b2 210000 N 2 120 E mm 12 1, 25 · 1, 25 34 ,54 t2 10 f y1 275 N 2 mm b1 b0 140 200 0 ,1 0 , 01 0 ,1 0 , 01 0 , 7 0 , 26 b0 t0 200 12 b2 b0 120 200 0 ,1 0 , 01 0 ,1 0 , 01 0 , 6 0 , 26 b0 t0 200 12 b1 140 14 35 t1 10 b2 120 12 35 t2 10 b0 200 15 16 , 667 35 t0 12 b1 b 2 140 120 0 ,6 1,3 0 , 6 1,3 0 , 6 0 ,92 1,3 2 b1 2·140 g 35 t 1 t 2 10 10 20 g 35 1,5·1 1,5·1 0 , 65 0 ,175 0 ,975 b0 200 g 35 0 ,5·1 0 ,5·1 0 , 65 0 ,175 0 ,175 b0 200 275 N 2· 12 10 f yo ·t 0 10 mm b eff · ·b1 · ·140 100 ,8 mm b 0 f y 1 ·t 1 200 275 N ·10 2 mm t0 12 275 N 2· 10 10 f yo ·t 0 10 mm b eff · ·b 2 · ·120 86 , 4 mm b 0 f y 1 ·t 2 200 275 N ·10 2 mm t0 12 J8 8 ,9 f yo t 0 b1 b 2 2 1 kn 0 ,5 N i , Rd sin( i ) 2 b o M 5 b0 200 8 . 33 2 t0 2 12 b1 h1 b 2 h 2 120 120 120 120 0 ,6 4b0 4·200 178 , 05 kN 42 , 07 10 mm 2 2 0 , Ed 3 275 10 kN k n 1( tension ) f yo mm 2 n1 0 ,154 0 , 4·n 0 , 4 0 ,154 M5 1 k n 1,3 1,3 1,197 1( comp ) 0 ,6 8 , 9 275 N 10 2 mm 2 120 120 1 1 2 53 º N 1 , Rd 2 200 8 , 33 1 530 , 698 kN 0 ,5 sin( 53 º ) 1 0 ,55 ·h o e 0 , 25 ·ho 0 ,55 ·200 30 0 , 25 ·200 110 30 50 b1 / 2 120 0 , 6 0 ,35 b0 200 b1 / 2 210000 N 2 120 E mm 12 1, 25 · 1, 25 34 ,54 t1 / 2 10 f y1 275 N 2 mm b1 / 2 b0 120 200 0 ,1 0 , 01 0 ,1 0 , 01 0 , 6 0 , 26 b0 t0 200 12 b1 / 2 120 12 35 t1 / 2 10 b0 200 15 16 , 667 35 t0 12 b1 b 2 120 120 0 ,6 1,3 0 , 6 1,3 0 , 6 1 1,3 2 b1 2·120 g 48 t 1 t 2 10 10 20 g 48 1,5·1 1,5·1 0 , 6 0 , 24 0 , 6 b0 200 g 48 0 ,5·1 0 ,5·1 0 , 6 0 , 24 0 , 20 b0 200 275 N 2· 12 10 f yo ·t 0 10 mm b eff · ·b i · ·120 86 , 4 mm b 0 f y 1 ·t i 200 275 N ·10 2 mm t0 12 J9 Strength to endure: 41,165t = 403,69kN Kind of Bolts: 8.8(fy=800N/mm2 and M20(As=245mm2 ; d=20mm; d0=22mm) 0 , 6· f y · A s 0 , 6·800 ·245 F v , Rd 94 ,1kN 1, 25 1, 25 403 , 69 kN Number of bolts = 4 , 29 bolts 6 bolts 94 ,1kN / bolt e1 1, 2·d 0 26 , 4 mm e 2 1,5·d 0 33 mm p 1 2 , 2·d 0 48 , 4 mm p 2 3 , 0·d 0 66 mm Also, we have to check the welding that is between the hollow profile and the small plate in each side. fu 3 f v ,Wd w M 2 fu tensile strength of steel plates welded γM2 = 1.25 partial safety factor of the welded joint βW correlation coefficient depending on the type of steel parts soldiers The throat thickness of fillet weld must be such that: a 0 , 7 e min a 0 , 7 12 mm a 8 , 4 mm We have taken a= 5mm. The length of the weld will be: F Ed Lw 2 a f v ,Wd 403 , 69 10 N 3 Lw 2 5 mm 222 , 7 N 2 mm L w 181 , 27 mm J10 Strength to endure: 86,218t = 845,51kN Kind of Bolts: 8.8(fy=800N/mm2 and M30(As=561mm2 ; d=30mm; d0=33mm) 0 , 6· f y · A s 0 , 6·800 ·561 F v , Rd 215 , 4 kN 1, 25 1, 25 845 ,51 kN Number of bolts = 3,92 bolts 4 bolts 215 , 4 kN / bolt e 1 1, 2·d 0 39 , 6 mm e 2 1, 5·d 0 49 . 5 mm p 1 2 , 2·d 0 72 . 6 mm p 2 3 , 0·d 0 99 mm Also, we have to check the welding that is between the hollow profile and the small plate in each side. fu 3 f v ,Wd w M 2 fu tensile strength of steel plates welded γM2 = 1.25 partial safety factor of the welded joint βW correlation coefficient depending on the type of steel parts soldiers The throat thickness of fillet weld must be such that: a 0 , 7 e min a 0 , 7 12 mm a 8 , 4 mm We have taken a= 5mm. The length of the weld will be: F Ed Lw 2 a f v ,Wd 845 , 51 10 N 3 Lw 2 5 mm 222 , 7 N 2 mm L w 379 , 66 mm J11 This type of joint only servant to join the two beams because these are very long. We put the screws are metric M20 minimal as they usually work in compression and only have the function of uniting the two parts. Strength to endure: 22,807t = 223,66kN Kind of Bolts: 8.8(fy=800N/mm2 and M20(As=245mm2 ; d=20mm; d0=22mm) 0 , 6· f y · A s 0 , 6·800 ·245 F v , Rd 94 ,1kN 1, 25 1, 25 223 . 66 kN Number of bolts = 2 ,37 bolts 4 bolts ( 2 and 2 ) 94 ,1kN / bolt e1 1, 2·d 0 26 , 4 mm e 2 1,5·d 0 33 mm p 1 2 , 2·d 0 48 , 4 mm p 2 3 , 0·d 0 66 mm Also, we have to check the welding that is between the hollow profile and the small plate in each side. fu 3 f v ,Wd w M 2 fu tensile strength of steel plates welded γM2 = 1.25 partial safety factor of the welded joint βW correlation coefficient depending on the type of steel parts soldiers The throat thickness of fillet weld must be such that: a 0 , 7 e min a 0 , 7 12 mm a 8 , 4 mm We have taken a= 5mm. The length of the weld will be: F Ed Lw 2 a f v ,Wd 223 , 66 10 N 3 Lw 2 5 mm 222 , 7 N 2 mm L w 100 , 43 mm J12 Strength to endure: 55,868t = 547,88kN Kind of Bolts: 8.8(fy=800N/mm2 and M20(As=245mm2 ; d=20mm; d0=22mm) 0 , 6· f y · A s 0 , 6·800 ·245 F v , Rd 94 ,1kN 1, 25 1, 25 547 . 88 kN Number of bolts = 5 ,82 bolts 8 bolts ( 4 and 4 ) 94 ,1kN / bolt e1 1, 2·d 0 26 , 4 mm e 2 1,5·d 0 33 mm p 1 2 , 2·d 0 48 , 4 mm p 2 3 , 0·d 0 66 mm Also, we have to calculate the welding part of each side. The resistance per unit area of the weld angle is equal to fV,Wd, whose value is derived from: fu 3 f v ,Wd w M 2 fu tensile strength of steel plates welded γM2 = 1.25 partial safety factor of the welded joint βW correlation coefficient depending on the type of steel parts soldiers The throat thickness of fillet weld must be such that: a 0 , 7 e min a 0 , 7 12 mm a 8 , 4 mm We have taken a= 5mm. The length of the weld will be: F Ed Lw 2 a f v ,Wd 547 ,88 10 N 3 Lw 2 5 mm 222 , 7 N 2 mm L w 246 , 01 mm ANNEX D: Checking and verification efforts in the shoe Having obtained feedback on the knots that form in encastaments land values are taken for the bending moment greater (M *) in the direction plan of the portico, the value of axillary major (N *) and shear value greater (T *). It first determinesm the eccentricity is subjected to the plate, using the equation: M M * M 22 , 22 tm e 0 , 251 m N * N N 88 , 218 t It makes the study of plate previously classified according to the eccentricity from in the following cases: 1. e<a/6 2. a/6<e<0.375a 3. e>0.375a a: is the largest of the lengths of the plate.=1000mm=1mm 1m 0 ,1666 0 , 251 m 0 . 375 ·1m 6 Considering the type of structure under study is necessary to follow the procedure pertaining to the case 2. The following is the calculation of checking one of the motherboards, specifically the type of the pillars of the portico. To make it checks the combination that has transmitted more than normal effort in the shoe of a pillar located approximately in the center of the ship. N Ed 88 , 218 t 865 ,1kN V Ed 0 , 231 t 2 , 27 kN M Ed 22 , 22 tm 217 ,97 kNm Value calculation of internal forces The conditions of equilibrium to determine the value calculation of internal forces. N Ed T Ed C Ed 0 N Ed T Ed ·a t C Ed ·a c 0 at: is the distance between the central axis of the bolt plate. In this case it 440 mm. ac: is the distance between the central axis of the plate and half the wing pillar. In this case is 300mm. M N Ed ·a c T Ed Ed 56,16kN ac at C Ed T Ed N Ed 808 ,95 kN Effective Area To calculate it, first find the value of a 1 and b1. These are the minimum values shown below: a1 5 a 5 m b1 5 b 4 m a 1 a h 1,12 m b1 b h 0 , 92 m The parameters used in these formulas are shown in the figure below: a=1m b=0,8m a1=1,12m b1=0,92 m Now you can calculate the concentration factor (k j) to be less than 5, the bearing resistance of the surface settlement (fjd) and the distance c which will calculate the effective area of the plate subjected to compression. a 1 ·b1 kj 1 . 135 5 a b 2 2 f j ·k j · f ck 1 . 135 15 N 2 11 . 35 N 2 3 3 mm mm 275 f yd 1 . 05 c tf 30 mm 85 mm 3 f jd 11 . 35 3 1 . 05 The effective area is the one white. In case checking will take another way because of having signs in both directions. In this case, therefore, c is the distance measured from the outer face of the signs. For the calculation, however, need to know the effective area subjected to compression. Therefore, it is considered the part marked with a red box. A eff , c 94000 mm 2 Strength Concrete C Ed Internal efforts: Ed 8,6 N 2 Aeff , c mm Local resistance to compression: C , Rd k j f cd 16 , 214 N 2 mm Ed C , Rd OK Strength of the motherboard (compressed area) c Internal efforts: M Ed Ed ·c· 31067 , 5 Nmm 2 mm 2 275 120 Resistance: M Rd f yd W 209 . 523 ,81 Nmm 1, 05 18 mm M Ed M Rd OK ANNEX E: Plans of the building

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