Question 3: Please refer to the metal bar and its cross-section shown below. Two strain gages a and and b are attached to the bar as shown; note that 3 is the angle of their orientation with the x-axis. Assume: the Young's modulus of the metal = 16, 500 ksi; the Poisson's ratio of the metal = 0.33; P, = 13 kips; P, = 20 kips; d = 4.0 in.; t = 0.75 in.; L = 18 in.; and B = 40°. Determine the strains expected in the strain gages.
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- uniform diameter d= 1.75 in. Segment (1) is an aluminum Ę₁ = 10000 ksi L₁ = 90 in. Segment (2) is a copper Ę₂ = 17000 ksi L₂ = 126 in. When Pis applied, a strain gage attached to copper segment (2) measures a normal strain of &2 = 1700 uin./in. in the longitudinal direction. What is the elongation of segment (1)? Answer in inch rounded-off to 3 decimal places L₁ A (1) Aluminum B L2 (2) CopperIf an isotropic material has a shear modulus of 125 Gpa and a Poisson's ratio of 0.2, calculate its Young's modulus. Select one: O E= 80 Gpa O E= 450 Gpa O E= 60 Gpa %3D O E= 30 Gpa %3D O E= 300 Gpa %3D If a rubber material is deformed as shown in the following figure, determine the normal strain along diagonal BD.Question 2 A 60° strain rosette is installed on the traction-free surface of a component with one of the strain gages aligned along the y-axis, as illustrated in Figure Q2. The gages show the following strain readings upon loading the structure: E, = 925 x10“ ; &, = 740 x10“ ; ɛ. = -555 ×106 (a) Determine the strains in the x-y directions and show the corresponding strain element. (b) Calculate the principal in-plane strains and the corresponding principal directions. Show the principal strain element. (c) Calculate the in-plane maximum shear strain and show the corresponding strain element. (d) If the structure is made of steel with elastic modulus and Poisson's ratio of 220 GPa and 0.30, respectively, calculate the principal stresses. Show the principal stress element. (e) Determine the normal strain in the n-direction. & Ea
- A circular aluminum tube of L=600mm is loaded in by compressive forces at its ends. The outside and inside diameters are 75mm and 63mm respectively. A strain gage is placed on the outside of the tube to measure nomal strains in the longitudinal direction. E=73 GPa and Poisson’s is 0.33. If the normal stress in the tube is 57 MPa, what is the load P? if the strain is 781 X 10-6, what is the shortening of the tube? What is the percent change in its cross-sectional If the tube in Problem #1 has a constant outer diameter of 75 mm along its entire length but has increased in inner diameter with a normal stress of 70 MPa over the middle third while the rest of the tube remains at 57 MPa and an additional the load of 15 kN is applied to the left at a point L/3, what is the inner diameter at the middle third if an additional load of 15kN is applied directed to the left at a point L/3 from the left, what is the inner diameter at the middle third.Calculate the moment and axial load capacity of the circular column corresponding to the given strain distributions. Use the formulas given below for the area and the centroid of circle segment. Column diameter D=2r= 500 mm 60 fek= 40 MPa Eco= 0.0021 mm/mm 140 E= 40000 MPa fy= 420 MPa 140 E= 200000 MPa 8-030 Area of one o30 bar= 707 mm2 60 a) Ec top= 0.003 mm/mm c= 200 mm b) Ecsop= 0.003 mm/mm c= 400 mmRigid 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 rod2. 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 rods
- 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.The strain in the x-direction at point A (shown in fig.) on the steel beam is measured and found to be ɛx = 139 x 106. The shear strain at point A is found to be yxY = R x 10° radians. The magnitude R is given by: (Take E= 204 GPa and Poisson's ratio =0.3). The cross-section of the beam is rectangular with depth 400mm and width 200mm respectively 100m 4ocmm 40om 600mnın 1000 mm 200mmA steel thick cylinder of external diameter 150 mm has two strain gauges fixed externally, one along the longitudinal axis and the other at right angles to read the hoop strain. The cylinder is subjected to an internal pressure of 75 MPa and this causes the following strains: (a) hoop gauge: 455 x 106 mm/mm tensile; (b) longitudinal gauge: 124 x 10 mm/mm tensile. Find the internal diameter of the cylinder assuming that Young's modulus for steel is 208 GPa and Poisson's ratio is 0.283.