The torsional assembly shown in figure below consists of a solid bronze (G3 45 GPa) shaft CD and a hollow aluminum alloy (GA = 28 GPa) shaft EF that has a steel (Gs 80 GPa) core. The ends C and F are fixed to rigid walls, and the steel core of shaft EF is connected to the flange at E so that the aluminum and steel parts act as a unit. The two flanges D and E are bolted together, and the bolt clearance permits flange D to rotate through 0.03 rad before EF carries any of the load. Determine the maximum shearing stress in each of the shaft materials when the torque T = 54 kN-m is applied to flange D. Hint: 0total = ec/D + 0D/E + BE/F= 0 !! %3! %3D %3D Answer: Shear stress of aluminium, bronze and steel are 52.9 MPa, 100.0 MPa and 75.6 MPa, respectively

The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 79 GPa] with a cross-sectional area of A₁ = 700 mm². Bar (2) is a bronze alloy [E = 106 GPa] with a cross-sectional area of A₂ = 480 mm². Assume L₁=1.8 m, L₂=2.1 m, a=0.5 m, b=1.6 m, and c=0.8 m. All bars are unstressed before the load P is applied; however, there is a 3.4-mm clearance in the pin connection at A. If a load of P = 53 kN is applied at B, determine: (a) the normal stresses 01, 02, in both bars (1) and (2). (b) the normal strains 1, 2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) A Answers: (a) σ₁ = (b) 1 (c) VA = i a L₁ B b (2) L2 MPa, 0₁ = με, €2 = mm. i i D MPa. με.

Problem 2 14600ksi, apr For the shown structure, AB is made by C83400-red-brass (Ebr 9.8 × 10-6/ °F) and BC is made by 2014-T6-aluminum (Eal 10600ksi, a al = 12.8 × 10-6/°F). AB and BC are joined at the collar B and fixed connected at their ends. The cross sectional area of each member is 1.75 in². If there is no load in the = member when T₁ 50 °F. Now the temperature for both members are increased to T₂ = 120 °F. Determine (1) Reaction forces at fixed end C (2) The average normal stress in the member AB (3) The average normal stress in the member BC (4) Eventually, how far will the collar B be displaced? = = 3 ft 2 ft

A rigid bar, AB, is pinned at point B. Two other bars, AC and AD, are connected to point A to provide support for AB. We are investigating the behavior of this system under a specific load. Key Details: Bar properties: Material: Steel with Young's modulus (Esteel) of 200 GPa and coefficient of thermal expansion (a) of 11.7 x 10^-6 /°C. Cross-sectional area: AC: 1960 mm² AD: 1250 mm² Length: AC: √2 meters (square root of 2 meters) AD: 1 meter Inclination angles: AC: θ₁ (theta 1) = 30° from horizontal AD: θ₂ (theta 2) = 20° from horizontal Load on bar AB: Idealized linearly increasing load with a maximum value of 30 kN/m at point B. Problem Objectives: Determine the internal forces (axial forces) acting within bars AC and AD due to the applied load on AB. Calculate the displacement of point A in both horizontal (dA,x) and vertical (dA,y) directions.If the bar is cooled by 10°C, what would be the:  Determine the internal forces (axial forces) acting within bars AC and AD…