The rigid bar shown is supported by axial bar (1) and by a pin connection at C. Axial bar (1) has a cross-sectional area of A₁ = 250 mm², an elastic modulus of E = 200 GPa, and a coefficient of thermal expansion of a = 11.3 x 10-6/°C. The pin at C has a diameter of 25 mm. After load P has been applied and the temperature of the entire assembly has been increased by 10°C, the total strain in bar (1) is measured as 775 μ (elongation). Assume L₁= 275 mm, a = 545 mm, b = 150 mm, and c = 265 mm. Determine (a) the magnitude of load P. (b) the average shear stress in pin C. C L₁ Connection detail (1) B Rigid bar D

Please show the formula used and free body diagram A rectangular steel block is 4 inches long in the x direction, 3 inches long in the y direction, and 4 inches long in the z direction. The block is subjected to a triaxial loading of three uniformly distributed forces as follows: 48 kips tension in the x direction, 60 kips compression in the y direction, and 54 kips tension in the z direction. If ν = 0.30 and E = 29 × 106 psi, determine the single uniformly distributed load in the x direction that would produce the same deformation in the y direction as the original loading.

A steel torsion bar AB with diameter d = 34 mm, and ductile material of tensile yield strength Sy = 276 MPa is attached to a rigid arm at A, supported by a bearing at C, and fixed at B, as the picture shows. At the right end of the arm is mounted the wheel on which the vertical force P acts from the ground and which passes through the center of the wheel. If bearing C acts as a simple support and the effect of transverse shear due to P is negligible, determine the maximum force P (in kN) that can be applied to the wheel. Consider a factor of safety n = 2.5. Use the maximum energy of distortion failure criterion and do the analysis on bar AB (torsion bar) in the section where the bearing is.