Question

(a). A rectangular cross section at a location along a beam in bending is acted upon by a bending moment and a shear force. The cross section is \(120 \mathrm{~mm}\) wide, \(300 \mathrm{~mm}\) deep and is orientated such that it is in bending about its major axis of bending. The magnitudes of the bending moment and shear force are \(315 \mathrm{kNm}\) and \(240 \mathrm{kN}\) respectively. Determine the maximum bending and shear stresses on the cross section. Plot the bending and shear stress distributions through the depth of the section at this cross section.

(b). Show that the midspan deflection for a simply supported beam, span \(L\), loaded by a uniformly distributed load ' \(w\) ' (load units/unit length), along its full length, is given by:

$$ \delta=\frac{5 w L^{4}}{384 E I} $$

where \(E\) is the Young's modulus of the beam material, and \(I\) is the second moment of area about the axis of bending.

(c). A simply supported steel beam spanning \(5.5 \mathrm{~m}\) supports a uniformly distributed load of \(16.3 \mathrm{kN} / \mathrm{m}\). The beam cross section is shown in Figure 3 . The Young's modulus of steel is \(210 \times 10^{3} \mathrm{~N} / \mathrm{mm}^{2}\). Calculate the mid-span deflection.

Answer 1