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i y « < m cQ o linearly elastic and have cross-sectional areas of 1800 mm2. E for the material of the members is 200000N/mm2.

The members of the framework are linearly elastic so that Eq. (4.17) may be written

or, since each member has the same cross-sectional area and modulus of elasticity

The solution is completed in Table 4.1, in which F are the member forces due to the actual loading of Fig. 4.8(a), FB f are the member forces due to the fictitious load PB f in Fig. 4.8(b) and FD f are the forces in the members produced by the fictitious load PDj in Fig. 4.8(c). We take tensile forces as positive and compressive forces as negative.

The vertical deflection of B is

1800 x 200000 and the horizontal movement of D is

The positive values of AB,V and AD h indicate that the deflections are in the directions of PB,f and PD f.

The analysis of beam deflection problems by complementary energy is similar to that of pin-jointed frameworks, except that we assume initially that displacements are caused primarily by bending action. Shear force effects are discussed later in the chapter. Figure 4.9 shows a tip loaded cantilever of uniform cross-section and length L. The tip load P produces a vertical deflection Av which we require to find.

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