Question # 3: The built-up beam is formed by welding together the thin plates of thickness 5 mm. Determine the location of the shear center O.

8 kN 4 m 15 kN 5 kN 2 m 2 kN 2 m 2 m A B с D E The aluminum rod shown has a diameter of 20 mm and is subject to axial forces acting at A, B, C, and D. Assume the rod has a Young's modulus of E = 70 GPa. a) State the internal axial forces within sections AB, BC, CD, and DE. Remember to indicate whether they are in tension or compression b) What is the displacement of A relative to C? c) What is the displacement of A relative to E?

The two vertical steel [E = 200 GPa] rods that support rigid bar ABCD are initially free of stress. Rod (1) has an area of A₁ = 350 mm² and a length of L₁ = 2.1 m. Rod (2) has an area of A₂ = 375 mm² and a length of L₂ = 1.5 m. Assume dimensions of a = 3.2 m, b = 1.1 m, and c = 1.4 m. After a load of P = 130 kN is applied to the rigid bar at D, determine: (a) the normal stresses in rods (1) and (2) (b) the magnitude of the downward deflection of the rigid bar at D. y,v (2) a L2 Rigid bar L₁ Answer: (a) σ₁ = i 02= i (b) VD= i (1) B MPa MPa mm -X,U b C ↓ С D P

The two vertical steel [E = 200 GPa] rods that support rigid bar ABCD are initially free of stress. Rod (1) has an area of A1 = 410 mm2 and a length of L1 = 3.2 m. Rod (2) has an area of A2 = 355 mm2 and a length of L2 = 1.3 m. Assume dimensions of a = 3.4 m, b = 1.2 m, and c = 1.5 m. After a load of P = 50 kN is applied to the rigid bar at D, determine: (a) the normal stresses in rods (1) and (2) (b) the magnitude of the downward deflection of the rigid bar at D. y,v (2) L2 a B C D x,u Rigid bar |(1) Answer: (a) o1 = i MPa 02 = i MPa (b) VD = i mm