4.1

Aluminum bars ( E = 30,000 ksi) are welded to rigid plates, as shown in Figure P4.1. All bars have a cross-sectional area of 0.5 in ². Due to the applied forces the rigid plates at A, B, C, and D are displaced in the x direction without rotating by the following amounts: u _A = ?0.0100 in, u _B = 0.0080 in, u _C = ?0.0045 in, and u _D = 0.0075 in. Determine the applied forces F ₁, F ₂, F ₃, and F ₄.

Figure P4.1

4.2

Brass bars between sections A and B, aluminum bars between sections B and C, and steel bars between sections C and D are welded to rigid plates, as shown in Figure P4.2. The rigid plates are displaced in the x direction without rotating by the following amounts: U _B = ?1.8 mm, U _C = 0.7 mm, and U _D = 3.7 mm. Determine the external forces F ₁, F ₂, and F ₃ using the properties given in Table P4.2.

Figure P4.2

4.3

The ends of four circular steel bars ( E = 200 GPa) are welded to a rigid plate, as...