(a) Figure Q2 shows a steel bar held between two rigid supports. The bar has a cross sectional area of 0.25 m? and is 6.0 m in length. The structure is stress free before a force P = 3×106 N is applied at the point shown. Steel has a Young's modulus E = 210 GPa and its coefficient of thermal expansion is equal to a = 12 ×10-6 K-1. (i) What is the stress in the bar to the left of the applied load? (ii) What change in temperature would cause the stress on the right of the applied load to go to zero? 4.0 m 2.0 m P Figure Q2 -Constrained metal bar.

If it is constrained between two supports A and B and is stress-free at 20 ℃, what would be the stress in the two materials when it is heated to 70 ℃, For Steel: Es = 210 GPa, Coefficient of expansion = 12x10^6/℃. For Brass: Eb = 105 GPa, Coefficient of expansion = 19x10^-6/℃

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…

A steel bar is held by two fixed supports as shown in the figure and is subjected to an increased temperature of AT = 200°C. If coefficient of thermal expansion and young's modulus of elasticity of steel are 11 x 10-6/°C and 200 GPa respectively, the magnitude of thermal stress (in MPa) induced in the bar is

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 = 95 GPa] with a cross-sectional area of A1 = 260 mm2. Bar (2) is an aluminum alloy [E = 69 GPa] with a cross-sectional area of A2 = 690 mm2. All bars are unstressed before the load P is applied; however, there is a 3-mm clearance in the pin connection at A. Assume L1 = 2000 mm, a = 1080 mm, b = 610 mm, c = 460 mm, and L2 = 1380 mm. If a load of P = 100 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.

Narrow bars of aluminum are bonded to the two sides of a thick steel plate as shown. Initially, at T₁ = 70°F, all stresses are zero. Knowing that the temperature will be slowly raised to T₂ and then reduced to T₁, determine (a) the highest temperature T₂ that does not result in residual stresses, (b) the temperature T₂ that will result in a residual stress in the aluminum equal to 58 ksi. Assume aa = 12.8 x 10-6/°F for the aluminum and a = 6.5 × 10-6/°F for the steel. Further assume that the aluminum is elastoplastic with E = 10.9 × 106 psi and ay = 58 ksi. (Hint: Neglect the small stresses in the plate.) Fig. P2.121