12 FORCE DISTRIBUTIONS Figure 127a illustrates the cross sec

1.2 FORCE DISTRIBUTIONS Figure 1.2-7(a) illustrates the cross section of a rectangular beam in bending. From elementary strength of materials, the internal force distribution corresponding to bending about the z axis is given by =-My/L , in units of force per unit area in the x direction, where M, is the bending moment about the z axis (force times length) and I, is the area moment of inertia about the z axis (given by I, Using area integration, prove that the net force in the x direction is zero and that the net moment about the z axis from this distribution is M.. Solution: Example | Example·2-1 1.2-1 bearm in bending. From Since the stress does not vary with respect to the z direction, isolate a dA area where dA = b dy, as shown in Fig. 1.2.7(b). If were positive in the x direction, as shown, the force on the dA area in the x direction would be d. The total force is found by integration across the entire area: The net moment about the z axis due to the force on the dA area is Integration across the entire area yields the net moment about the z axis. dA. M, bh3 h/2 However, 1.-bh3/12, and the moment about the z axis reduces to M.-M.. dy Figure 1.2-7

Solution

Actually as shown in above pictures its alredy given the strain formulas so directly put the value.I didnot get for which example you want solution but u can directly put the values in formula of ex-2.4.1