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.

2.58 Knowing that a 0.02-in. gap exists when the temperature is 75°F, determine (a) the temperature at which the normal stress in the alu- minum bar will be equal to -11 ksi, (b) the corresponding exact length of the aluminum bar. 0.02 in. - 14 in. - Bronze A = 2.4 in² E = 15 x 106 psi a = 12 x 10-6/°F Fig. P2.58 and P2.59 18 in.. Aluminum A = 2.8 in² E = 10.6 x 106 psi a = 12.9 x 10-6/°F 300 mm 0.5 mm 250