A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is made of steel (Es = 200 GPa, as = 11.7 × 10/°C) and portion BC is made of brass (E, = 100 GPa, ɑb =20.9 × 10° °C). Knowing that the rod is initially unstressed, determine (a) the axial stresses in portions AB and BC, when there is a temperature increase of 40°C, (b) the corresponding deflection at point B. 30-mm diameter 250 mm B -50-mm diameter 300 mm C

The brass rod AB is fixed connected at A. When the temperature is T₁-50 °C, there is a 3 mm gap between its end (point B) and the wall C. The cross-sectional area of the rod is 10 cm². Ignore the weight of the bar. The temperature is now increased to T₂-130 °C and the rod AB is pushing against the wall at C. Ebr = 100 GPa, abr = 20 x 10-6/°C Fallow 70 MPa L = 3m A 3 m B/C с 3 mm a. Draw a FBD for when the temperature is increased to T₂ and write down the force balance for this scenario. Call the reactions at FA and FC. Ton =1) und prit brolim volgen Aistis Intelesa si s b. State the compatibility condition and solve for the reactions at A and C.

H.W 3 Two aluminum alloy plates (2) are attached to the sides of a wooden beam (1) as shown in Figure 3. mensions of the composite cross section are b1 = 80 mm, d¡ = 240 mm, b2 = 10 mm, d2 = b2 The di- |di 120 mm, and a = 60 mm. Deter- (2) (2) %3D mine the maximum bending (1) a stresses produced in both the wooden beam and the aluminum b1 plates if a bending moment FIGURE 3 +6,000 N m is applied M2 %3D about the z axis. Assume that Ej = 12.5 GPa and E2 = 70 GPa.

A 5.2-m-long aluminum tube (1) is to be connected to a 2.2-m-long bronze pipe (2) at B. When put in place, however, a gap of 9 mm exists between the two members, as shown. Aluminum tube (1) has an elastic modulus of 69 GPa and a cross-sectional area of 1980 mm2. Bronze pipe (2) has an elastic modulus of 93 GPa and a cross-sectional area of 3970 mm2. If bolts are inserted in the flanges and tightened so that the gap at B is closed, determine: (a) the normal stresses ?1, ?2 produced in each of the members. (b) the displacement (change in length of material (2), up is positive) uB of flange B with respect to support A. 5.2 m 2.2 m Answers: (a) 0₁ = (b) Ug = C (1) B (2) -95.40 1.126 9 mm MPa, 0₂ = mm. -47.58 MPa