When an axial load is applied to the ends of the bar shown in the figure, the total elongation of the bar between joints A and C is 0.17 in. In segment (2), the normal strain is measured as 1,450 uin./in. Assume L₁ - 45 in. and L₂ - 94 in. Determine (a) the elongation of segment (2). (b) the normal strain in segment (1) of the bar. P A Answers: (a) in.6₂ = (b) £₁ = L₁ i i B (2) L2 in. uin./in.
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- An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.When an axial load is applied to the ends of the bar shown in the figure, the total elongation of the bar between joints A and C is 0.15 in. In segment (2), the normal strain is measured as 1,450 uin./in. Assume L₁ = 44 in. and L₂ = 82 in. Determine (a) the elongation of segment (2). (b) the normal strain in segment (1) of the bar. (1) P L₁ B (2) L2
- When an axial load is applied to the ends of the bar shown in the figure, the total elongation of the bar between joints A and C is 0.13 in. In segment (2), the normal strain is measured as 1,150 µin./in. Assume L1 = 38 in. and L, = 90 in. Determine (a) the elongation of segment (2). (b) the normal strain in segment (1) of the bar. P (1) P (2) B L1 L2 Answers: (a) in.82 = i in. (b) ɛ1 = i pin./in.When an axial load is applied to the ends of the bar shown in the figure, the total elongation of the bar between joints A and C is 0.19 in. In segment (2), the normal strain is measured as 1,900 pin./in. Assume L₁ = 42 in. and L₂ = 78 in. Determine (a) the elongation of segment (2). (b) the normal strain in segment (1) of the bar. P Answers: (a) in.6₂ = (b) Ex = (1) L₁ B (2) L2 in. uin./in. C PRigid 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)
- 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 2410 µm/m. Assume initial rod lengths of L₁ = 1,250 mm and L₂ = 2,000 mm. Determine the normal strain in rod (2). (1) 4₁ (2) Rigid bar O 975 μm/m O 1072 μm/m O 1757 µm/m O 1656 µm/m O 1506 μm/m B P 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.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 4150 μm/m. Assume initial rod lengths of L₁ = 1,250 mm and L2 = 2,000 mm. Determine the normal strain in rod (2). (1) 4₁ Rigid bar (2) O 2849 μm/m O 3261 µm/m O 3071 µm/m O 3584 µm/m O 2594 μm/m B P L₂ C (1)
- 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.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)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.