Remark regarding Problem:The relative importance of the strain energies UM in bending and...

Remark regarding Problem:The relative importance of the strain energies UM in bending and US in shear loading of beams is influenced by the ratio of the length L of the beam to its depth h, by the shape of the cross section, and by the type of loading. The relative magnitudes of UM and US are examined in Problem, for given ratios of L/h and given cross sections.

The simple beam with I-shaped cross section (S250 × 38, (Ix = 51.61 × 106 mm4, h = 254 mm, b = 7.9 mm; for the area, see footnote c of Table 5.1) shown in Figure P5.13 is made of steel (E = 200 GPa and G = 77.5 GPa). Show that

a. the length L must be greater than 35.1h for US < 0.01 UM,

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b. the length L must be greater than 15.7h for US < 0.05 UM

FIGURE P5. 13

TABLE 5 .1 Correction Coefficients for Strain Energy Due to Shear

aExact value.

bCalculated as the ratio of the shear stress at the neutral surface to the average shear stress.

cThe area A for the 1-section, channel, or box-section is the area of the web hb, where h is the section depth

and b the web thickness. The load is applied perpendicular to the axis of the beam and in the plane of the web.