A metal bar is made out of Ti-6A1-4V titanium (stiffness E = 120 GPa) and has a diameter d = 35 mm with the end at A fixed to the wall. There is a distributed axial load of w = 60 kN/m. Length of the bar is L1 = 1200 mm. Calculate the displacement of point A relative to the wall. L1 The displacement at A is 8 = mm w [kN/m] A cc 00 BY NO SA 2021 Cathy Zupke

L = 0.3m A = 20 x 6 mm E= 70 GPa allowable stress = 120 MPa 0.6 m 0.4 m 0.2 m Rigid bar D C W 0.5m 40 x 6 mm 50 GPa wable stress = 80 MPa 16 mm dia. bolt with allowable s 6 mm 80 MPa in bearing and 60 MPa The rigid bar A,B,C,D shown in figure is connected to the ground by a hinge at B and to Magnesium bar at A, Aluminum bar at C. the properties of the bars are shown on the figure. all the connections are using 16 mm bolts in single shear. Determine the maximum safe load W that can be applied. Determine the final position of point D.

The pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting bars. Bar (1) is a bronze alloy [E = 101 GPa] with a cross-sectional area of A₁ = 230 mm². Bar (2) is an aluminum alloy [E = 71 GPa] with a cross-sectional area of A₂ = 740 mm². All bars are unstressed before the load P is applied; however, there is a 4-mm clearance in the pin connection at A. Assume L₁ = 2040 mm, a = 1020 mm, b = 630 mm, c = 460 mm, and L₂ = 1470 mm. If a load of P = 155 kN is applied at B, determine (a) the normal stresses in both bars (1) and (2). (b) the downward deflection of point A on the rigid bar. (1) L₁ a b B Answers: (a) σ₁ = 02= (b) VA= i i i C MPa MPa mm (2) L2

A circular column is made of concrete [Ec = 4.2(103)ksi] while being reinforced with six steel rods [Est = 29 (103 )ksi]. It is acted upon by an axial force of 30 kip as shown in the figure to the right. Each rod has a diameter of 0.85 in.    c) Stress in each steel rod, σst = ____________________ ksi  d) Stress in the concrete, σc = ____________________ ksi