### Beams - Basic design - Steel Structures.

**1 Moment capacity, Mc**

The most basic design requirement for a beam is the provision of adequate in-plane bending strength. This is provided by ensuring that Mc for the selected section exceeds the maximum moment produced by the factored loading.Determination of Mc, which is linked to section classiﬁcation.

For a statically determinate structural arrangement, simple considerations of statics provide the moment levels produced by the applied loads against which Mc must be checked. For indeterminate arrangements, a suitable method of elastic analysis such as moment distribution or slope deﬂection is required. The justiﬁcation for using an elastically obtained distribution of moments with, in the case of compact or plastic cross-sections, a plastic cross-sectional resistance has been fully discussed by Johnson and Buckby.

**2 Effect of shear**

Only in cases of high coincident shear and moment, found for example at the internal supports of continuous beams, is the effect of shear likely to have a signiﬁcant inﬂuence on the design of beams.

Shear capacity Pv is normally calculated as the product of a shear strength pv, often taken for convenience as 0.6py which is close to the yield stress of steel in shear of 1/÷3 of the uniaxial tensile yield stress, and an appropriate shear area Av.

The process approximates the actual distribution of shear stress in a beam web as well as assuming some degree of plasticity.While suitable for rolled sections, it may not therefore be applicable to plate girders.An alternative design approach, more suited to webs containing large holes or having variations in thickness, is to work from ﬁrst principles and to limit the maximum shear stress to a suitable value; BS 5950: Part 1 uses 0.7py. In cases where d/t > 63, shear buckling limits the effectiveness of the web and reference to Chapter 17 should be made for methods of determining the reduced capacity.

In principle the presence of shear in a section reduces its moment capacity. In practice the reduction may be regarded as negligibly small up to quite large fractions of the shear capacity Pv. For example, BS 5950: Part 1 requires a reduction in Mc for plastic or compact sections only when the applied shear exceeds 0.6Pv, and permits the full value of Mc to be used for all cases of semi-compact or slender sections.

Figure 16.2 illustrates the application of the BS 5950: Part 1 rule for plastic or compact sections to a typical UB and UC having approximately equal values of plastic section modulus Sx. Evaluation of the formula in cases where Fv/Pv > 0.6 ﬁrst requires that the value of Sv, the plastic modulus of the shear area Av (equal to tD in this case), be determined. This is readily obtained from the tabulated values of S for rectangles given in Reference 2 corresponding to a linear reduction from Sx to (Sx - Sv).

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