100 N

Fig. 4.13 Framework of Example 4.4. Example 4.4

Calculate the loads in the members of the singly redundant pin-jointed framework shown in Fig. 4.13. The members AC and BD are 30 mm2 in cross-section, and all other members are 20 mm2 in cross-section. The members AD, BC and DC are each 800mm long. E = 200000N/mm2.

From the geometry of the framework ÄBD = CBD = 30°; therefore BD = AC = 800v^ mm. Choosing CD as the redundant member and proceeding from Eq. (4.22) we have

From Table 4.3 we have

Hence R = 2.1 N and the forces in the members are tabulated in column (7) of Table 4.3.

Table 4.3 (Tension positive)

Member

L (mm)

® 2 A (mm2)

F(N)

dF/dR

(.FL/A)dF/dR

Force (N)

0 0

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