H.W.7 A rigid steel bar ABC is supported by three rods. There is no strain in the rods before load P is applied. After load P is applied, the axial strain in rod (1) is 1,200 µɛ. (a) Determine the axial strain in rods (2). (b) Determine the axial strain in rods (2) if there is a 0.5 mm gap in the connections between rods (2) and the rigid bar before the load is applied.
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- Rigid bar ABCD is supported by two bars. There is no strain in the vertical bars before load P is applied. After load P is applied, the normal strain in bar (2) is measured as -3800 μm/m. Use the dimensions L₁ = 1900 mm, L₂ = 1425.00 mm, a = 190 mm, b = 380 mm, and c=143 mm. Determine: (a) the normal strain in bar (1). (b) the normal strain in bar (1) if there is a A = 1 mm gap in the connection at pin C before the load is applied. (c) the normal strain in bar (1) if there is a A = 1 mm gap in the connection at pin B before the load is applied. L₁ Answer: (a) &₁ = (b) E₁ = A i i (c) E₁ = i 1 1 1 a B (1) b Rigid bar L2 με με με C (2)2. A composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and length of the steel rod are given as 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0,53x 10-3. Given that the total extension of the composite rod must not exceed 0,162 4 mm and E for steel is 200 GPa, respectively. Calculate: d. Modulus of elasticity for the brass.2. A composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and length of the steel rod are given as 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0,53x 10-3. Given that the total extension of the composite rod must not exceed 0,162 4 mm and E for steel is 200 GPa, respectively. Calculate: a. Strain in the steel rod
- 2. A composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and length of the steel rod are given as 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0,53x 10-3. Given that the total extension of the composite rod must not exceed 0,162 4 mm and E for steel is 200 GPa, respectively. Calculate: a. Strain in the steel rod b. Load carried by the steel and brass rods d. Modulus of elasticity for the brass.2. A composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and length of the steel rod are given as 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0,53x 10-3. Given that the total extension of the composite rod must not exceed 0,162 4 mm and E for steel is 200 GPa, respectively. Calculate: b. Load carried by the steel and brass rodsThe stresses in a 2-D rectangular steel body (E = 200 GPa, v=0.32) are xx = -A(L - x)y, and oxy = A(h² - 4y²); other stress components are zero. Here, L represents length and h is height. What is the strain component y xy A - (h² - y²) 8E O A A 8G - (h²-x²) - (h²-x²) 8E А A= (h²-y:²) 8G ?
- Q3) The rigid bar ABCD is supported by bars (1) and (2). After load P is applied, the normal strain in bar (1) is 820 µm/m. Find (a) the normal strain in bar (2). (b) The normal strain in bar (2) if there is a 1-mm gap in the connection at pin C before the load is applied. (2) 300 mm 340 mm 140 mm 1200 mm B D 900 mm (1)A rigid steel bar is supported by three rods as shown. There is no strain in the rods before the load P is applied. After load P is applied, the normal strain in rods (1) is 2350 μm/m. Assume initial rod lengths of L₁ = 1,250 mm and L₂ = 2,000 mm. Determine the normal strain in rod (2). (1) A L₁ (2) Rigid bar 1721 μm/m 1858 μm/m O 1347 μm/m O 1469 μm/m 943 μm/m B L₂ (1)A rigid steel bar is supported by three rods, as shown. There is no strain in the rods before the load P is applied. After load P is applied, the normal strain in rod (2) is 1020 μin./in. Assume initial rod lengths of L1 = 148 in. and L2 = 78 in. Determine(a) the normal strain in rods (1).(b) the normal strain in rods (1) if there is a 0.043 in. gap in the connections between the rigid bar and rods (1) at joints A and C before the load is applied.(c) the normal strain in rods (1) if there is a 0.043 in. gap in the connection between the rigid bar and rod (2) at joint B before the load is applied.
- The bar ABC shown is loaded by a force P1=20 kN and P2= 40 kN at points C and B respectively. The bar has a constant axial rigidity of 120 x 10^6 N. A. Determine the strain energy of the bar when the force P1 acts alone (P2=0)B. Determine the strain energy of the bar when the force P2 acts alone (P1=0)C. Determine the strain energy when the forces P1 and P2 are acting simultaneously upon the bar.A circular aluminum tube of length L = 400 mm is loaded in compression by forces P as shown in Fig.2. The outside and inside diameters are 60 mm and 50 mm, respectively. A strain gage is placed on the outside of the bar to measure normal strain in the longitudinal direction. (a) If the measured strain is ε = 550×10-6, what is the shortening δ of the bar? (b) If the compressive stress in the bar is intended to be 40 MPa, what should be the load P?A circular aluminum tube of length L = 400 mm is loaded in compression by forces P as shown in Fig.2. The outside and inside diameters are 60 mm and 50 mm, respectively. A strain gage is placed on the outside of the bar to measure normal strain in the longitudinal direction. (a) If the measured strain is ε = 550×10-6, what is the shortening δ of the bar? (b) If the compressive stress in the bar is intended to be 40 MPa, what should be the load P? A car weighing 130 kN when fully loaded is pulled slowly up a inclined track by a steel cable as shown in Fig.2-b. The cable has an efficient cross sectional area of 490 mm2, and the angle of the incline is 30°. Please calculate the tensile stress σt in the cable.