Steel Beam Design Summary of the first lecture by bigbro22

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									                                                                           Summary notes


Steel Design for Bending and Shear
Steel beam design means:

-   predicting the behaviour of a section under load, in a particular situation,

-   checking that the section will not fail a set of performance criteria called limit
    states; strength and deflection are the most common,

-   selecting a section which can safely resist the applied actions

    ie.        Resistance           >       Applied action
               Moment capacity              Bending moment
               Shear capacity               Shear force

Factors governing behaviour under load:

-   Material

-   Actions (loads)

-   Support conditions

-   Section shape (properties)

Strength:

A steel beam can be considered as an arrangement of relatively thin plate elements.

The material properties and section geometry give each cross-section a set of
characteristics (section properties) which determine its behaviour under load.

The strength of a steel section is governed by failure in one or both of the following
modes:

-   Elastic buckling at stresses generally below yield strength py, when elastic section
    properties are used.

-   Plastic yielding where stresses reach the yield strength py in some areas of the
    section, when plastic section properties are used.

Steel sections may be subject to bending, shear, torsional, compressive and tensile
actions. Beams primarily resist bending and shear.

Design capacities:

The design of a steel beam involves comparing its moment and shear capacities with
the applied moments and shears derived from the loading arrangements.
The moment and shear capacities of a section are calculated from section properties,
which may be read from published tables or calculated from formulae.




Summary of the steel design for bending and shear                                        1
                                                                         Summary notes


Moment Capacity

The full moment capacity of a steel beam can only be achieved if :

   The compression flange is fully restrained

   Local buckling does not occur

Restraint

A system providing lateral restraint is considered adequate if it can resist a force equal
to 2.5% of the maximum factored force in the compression flange of the beam.

Section Class

Four classes are described in BS 5950 (Tables 11 and 12).

   Class 1 Plastic

   Class 2 Compact

   Class 3 Semi-Compact

   Class 4 Slender (rarely used)

Moment Capacity

                                                                     factoredload
Plastic                 :       Mc = p y  S    S  kZ         k=
                                                                    unfactoredload
Compact                 :

Semi-compact            :       Mc = py  Z

Slender                 :       Mc = p y ' Z

Where py' is a reduced value of py to give semi-compact proportions
                   1

            275  2
using:        
            p 
            y 

Elastic Moment Capactiy

M c  p y .Z x  M x (max. applied moment)

Zx is the Elastic Modulus

Plastic Moment Capacity (Low shear case)

M c  p y .S x  M x (max. applied moment)




Summary of the steel design for bending and shear                                    2
                                                                                  Summary notes

Sx is the Plastic Modulus


Plastic Moment Capacity (High shear case)

If Fv > 0.6Pv :

Mc = p y (S  S v )  M x (max. applied moment)

                          2
            F  
ρ        = 2 v   1
              
             Pv  

S       = plastic modulus of the whole cross section

                                                   t .D 2
Sv      = plastic modulus of the web alone =              for I or H sections
                                                      4

Shear Capacity

Pv  0.6p y .A v  Fv (max. applied shear force)

Deflection of Beams in Bending

    Elastic analysis is used for predicting deflections.

    If any material yields at service load levels then the beam will be permanently
     deformed when the load is removed.

    Standard formulae are given on the handout sheets.

    Remember that unfactored loads are used to calculate deflections because we
     want to know the actual likely deformation of the beam.

    The commonly adopted deflection limits are given in Table 8 BS 5950 - 2000.

                                                                                span
    The deflection of floor beams in buildings should be limited to ≤               , under
                                                                                360
     characteristic live loads.

    This limits potential damage to brittle finishes, services and partitions supported
     by the beam.

    If deflections appear excessive then it is possible to pre-camber the beam but it is
     more usual to increase the beam size or reduce the load in some way, e.g.
     position beams at closer centres.

    The problem of compound deflections also needs to be identified if deflection
     predictions are to have any meaning.




Summary of the steel design for bending and shear                                              3
                                                                   Summary notes


Design Procedure for Restrained Beams:

Our knowledge of restrained steel beam behaviour can be concisely summarized in
order for practical design to be carried out:
                                                                 BS 5950 ref.
1. Determine loadings.

2. Check restraint is adequate.                                  cl. 4.3.2

3. Calculate worst case bending moments and shear forces.        cl. 2.1.3 limit
   states

4. Select a trial section and determine py.                      Section property
                                                                 tables
                                                                 cl. 3.1.1 Table 9

5. Determine section class.                                      cl. 3.5.2
   (must not be slender)                                         Tables 11, 12

6. Check shear capacity:          Fv ≤ Pv = 0.6pyAv              cl. 4.2.3

7. Check moment capacity          Mmax ≤ Mc (plastic, compact)   cl. 4.2.5

           Low shear              Mc = py S (plastic, compact)

           High shear             Mc = py (S - ρSv)

8. Check deflections.                                            Table 8




Summary of the steel design for bending and shear                              4

								
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