The value of the shape factor can then be obtained as the ratio of the above equations Mfp/Me■ A typical value of shape factor for commercial rolled steel joists is 1.18, thus indicating only an 18% increase in "strength" capacity using plastic design procedures compared with the 50% of the simple rectangular section.

3.4. Partially plastic bending of unsymmetrical sections

Consider the T-section beam shown in Fig. 3.6. Whilst stresses remain within the elastic limit the position of the N.A. can be obtained in the usual way by taking moments of area

Stress distributions

Ptostic "na

(o) Elastic (b) Plastic about some convenient axis as described in Chapter 4.^ A typical position of the elastic N.A. is shown in the figure. Application of the simple blending theory about the N.A. will then yield the value of Me as described in the previous paragraph.

Whatever the state of the section, be it elastic, partially plastic or fully plastic, equilibrium of forces must always be maintained, i.e. at any section the tensile forces on one side of the N.A. must equal the compressive forces on the other side.

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