Document Sample

CSA Design of Structural Members with Formatted Spreadsheets Angus Chan Microsoft Excel spreadsheets with the use of pre-formatted macros CSA Design of Structural Members developed by former UBC students. The development of this with Formatted Spreadsheets project is used as a temporary substitute to CHEOPS due to difficulties from running the current version with Microsoft Windows Vista. Although the spreadsheet becomes a handy tool for the user to perform preliminary and quick checks of simple structural members, it lacks different section class checks and graphs provided from CHEOPS. In conclusion, the spreadsheet development is obviously lacking until a compatible update version of CHEOPS is readily available for Windows Vista users. Table of Contents Abstract .......................................................................................... 1 1.0 Introduction ............................................................................. 3 2.0 Objectives................................................................................. 3 3.0 Design of Compression Members .......................................... 3 3.1 Euler Buckling .................................................................. 4 3.2 Effective Length Concept (Ref. Appendix F)............. 5 3.3 Euler Buckling Stress ........................................................ 6 3.4 Inelastic Buckling ............................................................. 6 3.5 Effects of Geometric Imperfections .................................. 7 3.7 Slenderness Ratio Limit .................................................... 9 4.0 Design of Tension Members ................................................... 9 4.1 General Design Steps (ref. Clause 13.2) ........................... 9 4.2 Slenderness Ratio Limit (ref. Clause 10.4.2.2) ................. 9 Abstract 4.3 Effective Net Area, Ane (ref. Clause 12.3.3) ................... 10 Steel structure consists mainly of various types, including 5.0 Design of Bending Members ................................................ 11 compression, tension, bending, and bending-compression 5.1 Modes of Failure for Bending ......................................... 11 members. These are essential components of any type of structures 5.1.1 A. Local Section Requirement ............................. 11 and are designed by regulations such as the CSA. The design 1. Local flange buckling ........................................... 11 method developed through this project will be implemented in 2. Local torsional buckling of compression flange ... 11 angus_chan_CSA_Steel_Design 1/3/2008 PAGE 1 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 5.1.2 B. Overall Member Strength ................................ 11 12. Biaxial Bending Interaction (Class 1&2 I- Shaped 5.2 Lateral supports ............................................................... 11 Sections Only)............................................................... 13 5.3 Laterally Unsupported Members .................................... 11 6.3 Local Section Requirement ..................................... 13 5.4 Modes of Failure for Shear ............................................. 12 6.4 Combined Bending and Compression Stress Distribution for Prismatic Sections ........................................................... 14 6.5 Combined Bending and Compression Stress Distribution for I-Shaped Sections ............................................................ 14 6.7 Bending and Compression Interaction Curve for Class 1&2 I-Shaped Sections (Strong Axis)................................... 15 6.8 Bending and Compression Interaction Curve for Class 1&2 I-Shaped Sections (Weak Axis) .................................... 15 6.9 Moment Amplification: P-δ Effects............................... 16 6.10 Overall Member Strength Requirement for Braced Frames vs. Unbraced Frames ................................................ 17 6.10.1 B1a Cross Sectional Strength Requirement for Braced Frames .............................................................. 17 6.10.2 B1a.2 Cross-sectional strength for all classes except for Class 1& 2 I-shaped members (braced frames) 5.5 Limiting Shear Stress ...................................................... 12 ....................................................................................... 18 5.6 Shear Buckling ................................................................ 12 6.10.3 B2a In-plane Strength & Stability Requirement 6.0 Combined Bending and Compression Members ............... 13 for Braced Frames ......................................................... 18 6.1 Modes of Failure for Combined Bending and 6.10.4 B2a.2 In-plane member strength for all classes Compression ......................................................................... 13 except for Class 1& 2 I-shaped members (braced frames) 6.1.1 Local Section Requirement .................................. 13 ....................................................................................... 18 6.2 Overall Member Strength Requirement .......................... 13 6.10.5 B3a Lateral Stability Requirement for Braced 6.2.1 B1 Cross Sectional Strength Requirement ........... 13 Frames ........................................................................... 19 9. Overall section yielding ........................................ 13 6.10.6 B3a.2 Lateral torsional buckling strength for all 6.2.2 B2. In-plane Strength& Stability Requirement ... 13 classes of sections except for Class 1&2 I-shaped 10. In-plane stability ............................................... 13 members (braced frames) .............................................. 19 6.2.4 B3. Lateral Stability Requirement ....................... 13 6.10.7 B4a Biaxial Bending Strength Requirement for 11. Lateral torsional buckling ................................. 13 Braced Frames (Class 1& 2 Sections only) .................. 19 6.2.4 B4. Biaxial Bending Strength Requirement......... 13 6.10.8 B1b Cross Sectional Strength Requirement for Unbraced Frames .......................................................... 20 angus_chan_CSA_Steel_Design 1/3/2008 PAGE 2 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 6.10.9 B2b In-plane Strength & Stability Requirement complying fully with CSA design standards with reference to for Unbraced Frames..................................................... 20 structural development software, CHEOPS. 6.10.10 B2b.2 In-plane member strength for all classes except for Class 1& 2 I-shaped members (unbraced The design method developed through this project will be frames) .......................................................................... 20 implemented in Microsoft Excel spreadsheets with the use of pre- 6.10.11 B3b Lateral Stability Requirement for Unbraced formatted macros developed by former UBC students. The use of Frames ........................................................................... 20 automatic references to CISC shape tables is provides additional 6.10.12 B3b.2 Lateral torsional buckling strength for all advantages to design method, along with the flexibility for custom classes of sections except for Class 1&2 I-shaped modification or code changes. The spreadsheet platform is members (unbraced frames) .......................................... 21 intended for royalty-free means of distribution 6.10.13 B4b Biaxial Bending Strength Requirement for Unbraced Frames (Class 1& 2 Sections only) .............. 21 The development of this project is used as a temporary substitute 6.11 Second Order Effects due to Sway: P-Δ Effects ........... 22 to CHEOPS due to difficulties from running the current version 7.0 Conclusion ............................................................................. 22 with Microsoft Windows Vista. 8.0 Appendices ............................................................................. 23 References ............................................................................. 23 3.0 Design of Compression Members All compression members as used in practical applications generally fail in buckling. a. Local buckling can occur in the elements of shapes, such 1.0 Introduction as flanges or webs Steel structure consists mainly of various types, including b. Overall buckling limits the load carrying capacity of the compression, tension, bending, and bending-compression entire member. members. These are essential components of any type of structures The most common failure of compression members happens in the and are designed by regulations such as the CSA. inelastic buckling range. Only slender compression members behave linearly and fail according to the Euler theory. Slenderness This report focuses on the design methods of the various types of is defined as the ratio of compression member length over structural members to provide for a basic design tool for an minimum radius of gyration. Stresses are defined as the ratio of everyday user. loads over the cross sectional area. The maximum load of a practical compression member can vary considerably depending on 2.0 Objectives the initial out-of-straightness. Other imperfections such as residual The design procedure will comply with strength and stability stresses or change in geometry of the cross section can influence requirements as well as stiffness requirements to limit deflections the capacity of compression members, too. angus_chan_CSA_Steel_Design 1/3/2008 PAGE 3 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 3.1 Euler Buckling 2 y − EI d 2 = Cy ( x ) dx with C λ2 = EI we get d 2 y + 2 y( x) = 0 λ d x2 A solution for this differential equation is Compressive Element, Pinned Ends y(x) = A sin λ x + B cos λ x At any point at the centreline of the column we find: The constant A and B can be solved by considering the conditions EI = Cy ( x ) with ρ = curvature. at the boundaries of the compression member: ρ at x = 0 → y (x) = 0 → B = 0 2 − d 2 y resulting in 1 dx y = A sin λ x Then, = 3 ρ and at the other end of the column we find for ⎡ ⎛ dy ⎞ 2⎤ 2 ⎢1+ ⎜ ⎟ ⎥ at x = L → y (x) = 0 ⎢ ⎝ dx ⎠ ⎥ ⎣ ⎦ which can be solved by either A = 0 or sin λ L = 0 2 y − d 2 The first solution gives y (x) = 0 for any value of x, which means dx Therefore, EI 3 = Cy ( x ) the column would be straight. ⎡ ⎛ dy ⎞ 2⎤ 2 The second yields ⎢1+ ⎜ ⎟ ⎥ ⎢ ⎝ dx ⎠ ⎥ λ L = π , 2π , ... , n π ⎣ ⎦ This equation is not easy to solve. Therefore let’s assume the or deflections y(x) are small, then 2 EI 4 2 EI 2 2 C = π 2 , π 2 , . . . , n π2 EI L L L angus_chan_CSA_Steel_Design 1/3/2008 PAGE 4 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan The lowest load, the “Euler load”, at which the compression E = modulus of elasticity member is I = moment of inertia failing by buckling is π 2 EI Ce = The effective length, kL, may be thought of as the actual unbraced L2 length, L, multiplied by a factor, k, so that the product (kL) is 3.2 Effective Length Concept (Ref. Appendix F) equal to the length of a pin-ended compression member, Le, of the same capacity as the actual member. Columns may be designed using a simplified analysis utilizing the effective length concept. Pin-ended columns are employed as reference for comparison with columns having various end conditions. Once the strength of a pin-ended column is known, the strength of the same column with different end conditions can be obtained by KL L Le using the effective length factor, k. This effective length factor k equivalent to is defined as: k = Ce Ce C cr Ccr where the Euler buckling load of a pin-ended column with same Effective Length Concept for Axially Loaded Compression Members length is π 2 EI Ce = ( kL)2 and the critical load of end-restrained column 2 = π 2 EI C cr ( kL) Idealized Cases for Columns for which Joint Rotation and Translation are either fully realized or nonexistent with Le = length of pin-ended member L = member length angus_chan_CSA_Steel_Design 1/3/2008 PAGE 5 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 3.3 Euler Buckling Stress 3.4 Inelastic Buckling Euler’s theory covers only buckling situations where compressive stresses are below the elastic limit and are uniformly distributed over the complete cross section. Buckling of real compression members are influenced by geometric imperfections (initial out-of-straightness) and residual stresses. Design strength formula based on testing Cr=Φ •A • Fy (1+λ2n) –(1/n) angus_chan_CSA_Steel_Design 1/3/2008 PAGE 6 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 3.5 Effects of Geometric Imperfections angus_chan_CSA_Steel_Design 1/3/2008 PAGE 7 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 3.6 Effects of Residual Stresses In hot rolled shapes we usually find residual stress caused by uneven cooling speeds. Other sources of residual stresses in structural shapes may be cold bending or welding during fabrication and cutting operations or local plastic deformations such as punching of holes. 20% Fy 25% Fy ion compression compression pr ess m Co 45% Fy 30% Fy tension tension + 30% Fy tension + + 30% Fy Rolled W-shape compression Welded box Residual Stress in a Hot Rolled and Welded Structural Shapes angus_chan_CSA_Steel_Design 1/3/2008 PAGE 8 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 1. select tentative cross section using approximate 1. The separate effects of residual stress and initial curvature formulae and check slenderness ratio limit cannot be added. Tr = Φ Ag Fy 2. Residual stress has little effect on the maximum strength of very slender columns, either straight or initially crooked, 2. check design according to code requirements (least of which have strengths approaching the Euler load. the following): 3. Differences in maximum strength caused by variations in Tr = Φ Ag Fy or the shape of the residual-stress pattern are much smaller for Tr = 0.85Φ An Fu or initially curved columns than for initially straight columns. Tr = 0.85Φ Ane Fu • failure modes: 3.7 Slenderness Ratio Limit 1. excessive elongation (Fy governs) 2. rupture in net area (Fu governs) The value of slenderness ratio (KL/r) limit of 200 stems from experience. (ref. Clause 10.4.2.1 and Table 4-4) 3. rupture in effective net area (considers shear lag effects) • use “s2/4g - rule” for staggered bolt patterns 4.0 Design of Tension Members 4.2 Slenderness Ratio Limit (ref. Clause 10.4.2.2) Tension members act as principal structural members in trusses, bridges, transmission towers, bracing systems. They also have The value of slenderness ratio (KL/r) limit of 300 stems from applications as secondary members such as sag rods, bracing of experience and parallels values from foreign steel standards (i.e. OWSJs. It is most efficient because limit of usefulness not reduced German, Russian, American). by stability problems. Tension single shapes are most economical in applications, when doubling up use advantages of symmetry. All being said, limiting slenderness ratio exists because of potential of vibrations. 4.1 General Design Steps (ref. Clause 13.2) • design member in two steps: angus_chan_CSA_Steel_Design 1/3/2008 PAGE 9 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan Net Area, An by a factor of 0.6. (ref. Clause 12.3) 4.3 Effective Net Area, Ane (ref. Clause 12.3.3) This is applicable when critical net area includes the net area of unconnected elements For bolted connections: Ane = 0.60 to 0.90 An (refer to S16.1) For welded connections: Ane = An1 + An2 + An3 where bn = b - ∑D + ∑s2/(4g) An1 for elements connected by transverse welds An2 for elements connected by longitudinal welds along where two parallel edges An3 for elements connected by a single longitudinal weld d = bolt diameter D = d + 2mm for drilled holes D = d + 4mm for punched holes Note: if shear block failure is involved, reduce shear path g1 P P d h g2 e s2 s1 angus_chan_CSA_Steel_Design 1/3/2008 PAGE 10 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 5.2 Lateral supports 5.0 Design of Bending Members Bending members have its application in being the principal structural members in roof beams, floor beams, bridge decks, etc. most space efficient because of low height to span ratio. Furthermore, lateral torsional buckling is the most important mode of failure for laterally unsupported bending members 5.1 Modes of Failure for Bending 5.1.1 A. Local Section Requirement ref. Clause 11.2, Table 2, Table 5-1) 1. Local flange buckling 2. Local torsional buckling of compression flange 5.3 Laterally Unsupported Members 3. Local web buckling 5.1.2 B. Overall Member Strength Laterally supported: (ref. Clause 13.5) 4. Yielding (full section vs. flange only) Laterally unsupported: (ref. Clause 13.6) 5. Lateral torsional buckling angus_chan_CSA_Steel_Design 1/3/2008 PAGE 11 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 5.4 Modes of Failure for Shear 1) Yielding (shear area) 2) Shear buckling (web) 5.5 Limiting Shear Stress Full yielding followed by strain-hardening: Fs=0.66•Fy Yielding in shear in accordance with von Mises criterion: Fvy=0.577•Fy 5.6 Shear Buckling The modes of shear buckling includes 2 types: • Inelastic buckling: Fcri • Elastic buckling: Fcre angus_chan_CSA_Steel_Design 1/3/2008 PAGE 12 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 6.0 Combined Bending and Compression 9. Overall section yielding Members 6.2.2 B2. In-plane Strength& Stability Requirement These structural members include columns, top chord of trusses, (ref. Clause 13.8.2(b), 13.8.3(b)) and principal members in vierendeel trusses and rigid frames. Its 10. In-plane stability eccentricity of the applied load, or initial curvature of the column axis always generate bending moments. The UDL on top chord of 6.2.4 B3. Lateral Stability Requirement a truss generate moments and compression loads in members. Rigid frames and Vierendeel trusses generate bending moments (ref. Clause 13.8.3(c), 13.8.3(c)) and compression loads in members. The distinction of this 11. Lateral torsional buckling structural member is made between braced and unbraced frames 6.2.4 B4. Biaxial Bending Strength Requirement (ref. Clause 13.8.2) 6.1 Modes of Failure for Combined Bending and 12. Biaxial Bending Interaction (Class 1&2 I- Shaped Compression Sections Only) 6.1.1 Local Section Requirement 6.3 Local Section Requirement (ref. Clause 11.2, Table 2, Table 5-1) (ref. Clause 11.2, Table 2, Table 5-1) 6. Local flange buckling Flanges: 7. Local torsional buckling of compression flange Same as for bending members Webs: 8. Local web buckling Limiting h/w ratios depend on value of Cf/Cy Where 6.2 Overall Member Strength Requirement Cf = the applied factored axial load Cy = A· Fy 6.2.1 B1 Cross Sectional Strength Requirement (ref. Clause 13.8.2(a), 13.8.3(a)) Note: see Table 4-1 for typical limiting ratio values angus_chan_CSA_Steel_Design 1/3/2008 PAGE 13 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 6.4 Combined Bending and Compression Stress 6.5 Combined Bending and Compression Stress Distribution for Prismatic Sections Distribution for I-Shaped Sections Bending and Compression Interaction Curve for Prismatic Sections angus_chan_CSA_Steel_Design 1/3/2008 PAGE 14 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 6.7 Bending and Compression Interaction Curve for Class 1&2 I-Shaped Sections (Strong Axis) 6.8 Bending and Compression Interaction Curve for Class 1&2 I-Shaped Sections (Weak Axis) angus_chan_CSA_Steel_Design 1/3/2008 PAGE 15 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 6.9 Moment Amplification: P-δ Effects L2 Cf δ II = 2 ⋅ C f ⋅δ = δ π ⋅ EI Ce Where π 2 ⋅ EI Ce = L2 , Euler Buckling load δ = δo+δII Therefore, Cf δ o = δ ⋅ (1 − ) M=Mo+Cf·v Ce v = vo+vII δo 2 d vII π ⋅z δ = − EI = C f ⋅ δ ⋅ sin ⎛ Cf ⎞ dz 2 L ⎜1 − ⎜ C ⎟ ⎟ Where ⎝ e ⎠ δ is the maximum deflection at midspan z=L/2 Mmax=Momax+Cf·δ 2 L π ⋅z vII = ⋅ C f ⋅ δ ⋅ sin π 2 ⋅ EI L angus_chan_CSA_Steel_Design 1/3/2008 PAGE 16 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan on Eurocode 3) Pδ effects important and moment amplification ⎛ Cf ⎞ factor, U1, applies ⎜1 + ϕ ⎜ ⎟ ⎝ Ce ⎟ ⎠M Unbraced Frames M max = o max frames without direct acting bracing, or with bracing of sway ⎛ Cf ⎞ stiffness less than 5 times that of the frames without direct acting ⎜1 − ⎜ C ⎟ ⎟ bracing. Pδ effects negligible and moment amplification factor, ⎝ e ⎠ U1, does not apply (U1=1). This is because the maximum second- order elastic moment, including P∆ effects, occurs at the ends of the beam-column. δ o ⋅ Ce ϕ= −1 M o max 6.10.1 B1a Cross Sectional Strength Requirement for Braced Frames Cf B1a.1 Cross-sectional strength for Class 1& 2 I-shaped ω1 = 1 + ϕ members (braced frames) Ce Cf 0.85 ⋅ U1x M fx 0.6 ⋅ U1 y⋅ ⋅ M fy ω1 + + ≤ 1.0 M max = M o max = U1 ⋅ M max Cr M rx M ry ⎛ Cf ⎞ ⎜1 − ⎜ C ⎟ ⎟ Note: ⎝ e ⎠ λ y = 0 , β = 0 .6 + 0 .4 ⋅ λ y = 0 .6 6.10 Overall Member Strength Requirement for Cr = φ ⋅ A ⋅ Fy (Clause 13.3.1) Braced Frames vs. Unbraced Frames M r = φ ⋅ Z ⋅ Fy (Clause 13.5) Braced Frames frames with direct acting bracing that provides sway stiffness at U1x & U1 y ≥ 1 (Clause 13.8.2a, 13.8.4) least 5 times that of the frames without direct acting bracing (based angus_chan_CSA_Steel_Design 1/3/2008 PAGE 17 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 6.10.2 B1a.2 Cross-sectional strength for all classes K ⋅L Fy except for Class 1& 2 I-shaped members (braced λy = frames) ry π2 ⋅E , Cf + U 1x M fx + U 1 y⋅ ⋅ M fy ≤ 1.0 β = 0 .6 + 0 .4 ⋅ λ y Cr M rx M ry ( C r = φ ⋅ A ⋅ Fy ⋅ 1 + λ x ) 2 n −1 / n (Clause Note: 13.3.1) λ =0 M r = φ ⋅ Z ⋅ Fy (Clause 13.5) Cr = φ ⋅ A ⋅ Fy (Clause 13.3.1) U1x & U1 y (Clause 13.8.2b, 13.8.4) M r = φ ⋅ Z ⋅ Fy or φ ⋅ S ⋅ Fy (Clause 13.5) 6.10.4 B2a.2 In-plane member strength for all U1x & U1 y ≥ 1 (Clause 13.8.3a, 13.8.4) classes except for Class 1& 2 I-shaped members (braced frames) 6.10.3 B2a In-plane Strength & Stability Requirement for Braced Frames Cf U 1x M fx U 1 y⋅ ⋅ M fy + + ≤ 1.0 Cr M rx M ry B2a.1 In-plane member strength for Class 1& 2 I-shaped members (braced frames) Note: Cf 0.85 ⋅U 1x M fx β ⋅U 1 y⋅ ⋅ M fy K =1 + + ≤ 1.0 Cr M rx M ry K ⋅L Fy λx = Note: rx π2 ⋅E , K =1 Cr = φ ⋅ A ⋅ Fy ⋅ 1 + λ x( ) 2 n −1 / n (Clause 13.3.1) angus_chan_CSA_Steel_Design 1/3/2008 PAGE 18 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan M r = φ ⋅ Z ⋅ Fy or φ ⋅ S ⋅ Fy (Clause 13.5) 6.10.6 B3a.2 Lateral torsional buckling strength for all classes of sections except for Class 1&2 I- U1x & U1 y (Clause 13.8.3b, 13.8.4) shaped members (braced frames) Cf U 1x M fx U 1 y⋅ ⋅ M fy 6.10.5 B3a Lateral Stability Requirement for Braced + + ≤ 1.0 Cr M rx M ry Frames Note: B3a.1 Lateral torsional buckling strength for Class 1& 2 I- shaped members (braced frames) K ⋅L Fy λ= Cf 0.85 ⋅U 1x M fx β ⋅U 1 y⋅ ⋅ M fy r π2 ⋅E , + + ≤ 1.0 Cr M rx M ry Cr = φ ⋅ A ⋅ Fy ⋅ 1 + λ2 n( )−1 / n (Clause 13.3.1) Note: 0.28 ⋅ M P M r = 1.15 ⋅ φ ⋅ M P ⋅ (1 − ), K ⋅L Fy Mu λy = ry π2 ⋅E , or φ ⋅ MU (Clause 13.6) β = 0 .6 + 0 .4 ⋅ λ y U1x ≥ 1 & U1 y (Clause 13.8.3c, 13.8.4) ( Cr = φ ⋅ A ⋅ Fy ⋅ 1 + λ2 n ) −1 / n (Clause 13.3.1) 6.10.7 B4a Biaxial Bending Strength Requirement for Braced Frames (Class 1& 2 Sections only) 0.28 ⋅ M P M r = 1.15 ⋅ φ ⋅ M P ⋅ (1 − ), Mu M fx M fy + ≤ 1 .0 or φ ⋅ MU (Clause 13.6) M rx M ry U1x ≥ 1 & U1 y (Clause 13.8.2c, 13.8.4) angus_chan_CSA_Steel_Design 1/3/2008 PAGE 19 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 6.10.8 B1b Cross Sectional Strength Requirement 6.10.10 B2b.2 In-plane member strength for all for Unbraced Frames classes except for Class 1& 2 I-shaped members (unbraced frames) For this type of frames, strength Check not Required Cf M fx M fy + + ≤ 1 .0 Cr M rx M ry 6.10.9 B2b In-plane Strength & Stability Requirement for Unbraced Frames Note: K =1 ( ) B2b.1 In-plane member strength for Class 1& 2 I-shaped 2 n −1 / n members (unbraced frames) C r = φ ⋅ A ⋅ Fy ⋅ 1 + λ x (Clause Cf 0.85 ⋅ M fx β ⋅ M fy 13.3.1) + + ≤ 1.0 M r = φ ⋅ Z ⋅ Fy or φ ⋅ S ⋅ Fy (Clause 13.5) Cr M rx M ry U1x & U1 y = 1 (Clause 13.8.3b) Note: K =1 6.10.11 B3b Lateral Stability Requirement for Unbraced Frames K ⋅L Fy λy = rr π2 ⋅E , B3b.1 Lateral torsional buckling strength for Class 1& 2 I- shaped members (unbraced frames) β = 0 .6 + 0 .4 ⋅ λ y Cf 0.85 ⋅ M fx β ⋅ M fy C r = φ ⋅ A ⋅ Fy ⋅ 1 + λ x( ) 2 n −1 / n (Clause Cr + M rx + M ry ≤ 1.0 13.3.1) Note: M r = φ ⋅ Z ⋅ Fy (Clause 13.5) U1x & U1 y = 1 (Clause 13.8.2b) angus_chan_CSA_Steel_Design 1/3/2008 PAGE 20 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 0.28 ⋅ M P K ⋅L Fy M r = 1.15 ⋅ φ ⋅ M P ⋅ (1 − ), λy = Mu rr π2 ⋅E , or φ ⋅ MU (Clause 13.6) β = 0 .6 + 0 .4 ⋅ λ y U1x & U1 y = 1 (Clause 13.8.3c) Cr = φ ⋅ A ⋅ Fy ⋅ 1 + λ ( ) 2 n −1 / n (Clause 13.3.1) 6.10.13 B4b Biaxial Bending Strength Requirement 0.28 ⋅ M P M r = 1.15 ⋅ φ ⋅ M P ⋅ (1 − ), for Unbraced Frames (Class 1& 2 Sections only) Mu M fx M fy or φ ⋅ M U (Clause 13.6) + ≤ 1 .0 M rx M ry U1x & U1 y = 1 (Clause 13.8.2c) 6.10.12 B3b.2 Lateral torsional buckling strength for all classes of sections except for Class 1&2 I- shaped members (unbraced frames) Cf M fx M fy + + ≤ 1 .0 Cr M rx M ry Note: K ⋅L Fy λ = r π2 ⋅E , ( Cr = φ ⋅ A ⋅ Fy ⋅ 1 + λ2 n ) −1 / n (Clause 13.3.1) angus_chan_CSA_Steel_Design 1/3/2008 PAGE 21 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 6.11 Second Order Effects due to Sway: P-∆ Effects ∆f = the lateral displacement at the level considered relative to the level below h = the height of the storey between these two levels ∑Cf = sum of the columns axial load at the storey ∑Vf = storey shear Mfg = factored first-order moment resulting from gravity load Mft = factored first order moment resulting from lateral loads 7.0 Conclusion The structural members are designed in almost every type of building ever existed. With the information provided in the design code, the designs can be implemented into Microsoft Excel formatted spreadsheets. The use of automatic reference of CISC shape tables enhances the flexibility for custom modification or code changes by the interface user. While the spreadsheet is designed for easy usage and meant to be royalty-free, this project can allow act as an temporary substitute for the CHEOPS software. The spreadsheet becomes a handy tool for the user to perform preliminary and quick checks of simple structural members. But Mf=Mfg+U2·Mfg lacking different section class checks and graphs provided from CHEOPS, the spreadsheet development is obviously lacking until a Where compatible update version of CHEOPS is readily available for Windows Vista users. ω1 U2 = ⎛ ∑Cf Δ f ⎞ ⎜1 − ⎟ ⎜ ∑V f h ⎟ ⎝ ⎠ angus_chan_CSA_Steel_Design 1/3/2008 PAGE 22 OF 23 CSA Design of Structural Members with Formatted Spreadsheets Angus Chan 8.0 Appendices References [1] Cheops, Maplesoft Development Corp, 1998-2001 [2] Siegfried F. Stiemer, Dr.-Ing.(Ph.D.), University of British Columbia angus_chan_CSA_Steel_Design 1/3/2008 PAGE 23 OF 23

DOCUMENT INFO

Shared By:

Categories:

Tags:
Graphic Apps, Design Spreadsheets, steel pipe, steel building, steel plate, steel mill, steel city, 3D CAD design, Form Filler, Games & Entertainment

Stats:

views: | 338 |

posted: | 11/14/2010 |

language: | English |

pages: | 23 |

Description:
Steel Design Spreadsheets Holes document sample

OTHER DOCS BY ija53857

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.