The state of plane strain on an element has components € =-410(10-6), ey = 0, and %3D Yæy = 190(10–6). (Figure 1)
Q: 11. What is the strain on a metal bar (original length 10 cm) if it is now 12 cm long? A. 1.2 B.…
A: Ans.11 Given Data Original length = 10cm Final length =12 cm
Q: *10-12. The state of strain on an element has components e, = -400(10-9), e, = 0, ysy = 150(10-").…
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Q: 6. Determine the lateral strain, in mm/mm, in the 5 mm diameter aluminum T6 rod when P = 8 kN. Use L…
A: Given:P=8 KNL=400 mmν=0.35E=70 GPa
Q: The state of strain at the point on the spanner wrench has components of Px = 260(10-6), P y =…
A: Given data: Normal strain in x direction, εx = 260 x 10-6 Normal strain in y direction, εy = 320 x…
Q: 10-11. The state of strain on an element has components q = -150(10-9), e, = 450(10-9). Yay =…
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Q: The state of strain on an element has components Px = -300(10-6), Py = 100(10-6), gxy = 150(10-6).…
A: Given Data: The x component of the normal strain is: εx=-300 X 10-6. The x component of the normal…
Q: A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are εx = 0.40…
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Q: A rigid steel bar is supported by three rods as shown. There is no strain in the rods before the…
A: Normal stress is defined as the intensity of force exerted on the cross sectional area of a member.…
Q: Transform the set of cartesian strain components (, = 400 µe (y = 250 µe „ = 125 pe %3D %3D 7ay =…
A: Solution:
Q: Determine the average normal strain that occurs along the diagonals AC and DB.
A: Consider the points A, B and C becomes A’, B’ and C’ as shown in the below figure. Evaluate the…
Q: A specimen consists of a rigid member CBD and a flexible cable AB. A: Determine the normal strain in…
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Q: A rigid steel bar is supported by three rods, as shown. There is no strain in the rods before the…
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Q: The steel shaft has a radius of 15 mm. Determine the torque T in the shaft if the two strain gages,…
A: Write the given data:
Q: Q4) The 60° strain rosette is mounted on a beam. The following readings are obtained from each…
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Q: Determine the strain if a rod is experiencing a stress of 70,000 kPa with a modulus of elasticity of…
A: Determine the strain
Q: The distributed loading is applied to the rigid beam, which is supported by the three bars. Each bar…
A: Due to the distributed load the bars will experience equal force. Let the force in each bar be F.…
Q: The strain at point A on the bracket has normal components 250x10-6 and 550x10-6 in x and y…
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Q: A rigid horizontal bar ABC is supported by three vertical rods. There is no strain in the rods…
A: To find: The value of vB and ε2. Given Data : Axial strain in rod (1) is ε1 = 580.00 με. Length of…
Q: For the strain element shown below, a. determine the strain components for the (x, y) coordinate…
A: For the strain element shown below, a. determine the strain components for the (x, y) coordinate…
Q: Part of a control linkage for an airplane consists of a rigid member CB and a flexible cable AB. If…
A: Given Data∆AB=0.00317 mm AC=600mm BC=800mm
Q: The strain at point A on the bracket has normal components 200x106 and 400x106 in x and y…
A: Option (c) 501.6 is correct option
Q: A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are…
A:
Q: If a rubber material is deformed as shown in the following figure, determine the normal strain along…
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Q: The 45° strain rosette is mounted on the surface of a shell. The following readings are obtained for…
A: Given that,εa=-200×10-6εb=300×10-6εc=250×10-6Here,εx=εc=250×10-6εy=εa=-200×10-6
Q: The state of plane strain on an element has components e,= Tay = 110(10 ). (Eigure 1) -480(10-6), e,…
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Q: The strain at point A on the bracket has normal components 400x10-6 and 550x10-6 in x and y…
A: Given Data: strain at point A=∈x=400×10-6∈y=550×10-6 Vxy=-650×10-6
Q: he center portion of the rubber balloon has a diameter of d 100 mm. If the air lessure within it…
A: Given data : original diameter=100 mmfinal diameter=125 mm
Q: The state of strain on an element has components εx=−270(10−6)εx=−270(10−6),…
A:
Q: Prove that the sum of the normal strains in perpendicular directions is constant, i.e., Px + Py =…
A: Let strain in x and y directions are Px and Py respectively. strain in x` and y` directions are Px`…
Q: The state of strain at the point on the bracket has components Px = 350(10-6), Py = -860(10-6),gxy =…
A: Given data: The x component of strain is Px = 350 x 10-6. The y component of strain is Py = -860 x…
Q: Transform the set of cartesian strain components , = 400 µe y = 250 µe 125 µe %3D 275 µe %3D Yy: =…
A: Solution:
Q: 7- The state of strain at the point has components in the X-axis = -210x10-6, in the y-axis =…
A:
Q: 1.The force applied at the handle of the rigid lever causes the lever to rotate clockwise about the…
A: Draw the diagram in that the lever is rotated by 2 degrees clockwise.
Q: The state of strain at a point on the bracket has components of Px = 150(10-6), Py = 200(10-6), gxy…
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Q: The wire AB is unstretched when 8 = 45°, If a force is applied downward to end A of the bar AC,…
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Q: A pipe is subjected to a tension force of P = 70 kN. The pipe outside diameter is 32 mm, the wall…
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Q: The bar is made of an aluminum alloy having a stress–strain diagram that can be approximated by the…
A: Given Data: The maximum strain in the top and bottom fiber is εmax=0.05. The stress corresponding…
Q: PROBLEM 1. The state of strain at a point on an experimental aircraft wing has components, E. = 300…
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Q: The rigid beam is supported by a pin at A and wires BD and CE. If the load P on the beam causes the…
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Q: The strain at point A on the bracket has normal components 550x106 and 550x106 in x and y…
A: Option d is correct.
Q: 10–11. The state of strain on an element has components €x = -150(10-6), €, = 450(10-"), Yxy =…
A:
Q: The strain at point A on the bracket has normal components 750x106 and 150x106 in x and y…
A:
Q: 60 min 24 mm 180 mm O1// Determine the principles strain for the point (A) of the bar which 32 mm…
A: given; axial force in x-direction(Fx)=1KN (tensile)…
Q: The material distorts into the dashed position shown. Determine the average normal strains Px, Py…
A: Find out the normal strain in x-direction εx=A'F'-AFAF=150-150150=0 Find out the normal strain in…
Q: The strain components ex = 466 µE, ey = -524 µe, and yxy = -646 µrad are given for a point in a body…
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Q: 5. A material is subjected to principal stresses o, and o,. Determine the orientation 6 of a strain…
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Q: When an axial load is applied to the ends of the bar shown, where L₁ = 30 in. and L₂ = 80 in., the…
A: Given data: L1 = 30 in and L2 = 80 in Total Elongation = 0.1 in Normal strain in segment (1) =…
Q: A rigid steel bar is supported by three rods as shown. There is no strain in the rods before the…
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Q: Question 1: The state of strain at the point on the pin leaf has components of Ex = 200(106), E =…
A: Write the given data. εx=200×10-6εy=180×10-6γxy=-300×10-6 Calculate the principle strains.…
Q: The strain gauge is placed on the surface of a thin- walled steel boiler as shown. If it is 0.5 in.…
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Determine the equivalent state of strain on an element at the same point oriented 30∘∘ clockwise with respect to the original element.
ϵx′, ϵy′,γx′y′ =
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- A hollow circular tube A fits over the end of a solid circular bar B, as shown in the figure. The far ends of both bars are fixed. Initially, a hole through bar B makes an angle ß with a line through two holes in tube A. Then bar B is twisted until the holes are aligned, and a pin is placed through the holes. When bar B is released and the system returns to equilibrium, what is the total strain energy U of the two bars? (Let lAand lBrepresent the polar moments of inertia of bars A and B, respectively. The length L and shear modulus of elasticity G are the same for both bars.)The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the gage angle is ß = 750, the measured strains are = 209 × 10-6 and B = -110 × 10, and the material is a magnesium alloy with modulus E = 6.0 X 106 psi and Poisson’s ratio v = 0.35.
- A bungee cord that behaves linearly elastically has an unstressed length L0= 760 mm and a stiffness k = 140 N/m. The cord is attached to two pegs, distance/? = 380 mm apart, and is pulled at its midpoint by a Force P = 80 N (see figure). (a) How much strain energy U is stored in the cord? (b) What is the displacement Scof the point where the load is applied? (c) Compare the strain energy (with the quantity PSC12. Note: The elongation of the cord is not small compared lo its original length.An clement of material subjected to plane strain (see figure) has strains of x=280106 , y=420106 , and xy=150106 . Calculate the strains for an element oriented at an angle = 35°. Show these strains on a sketch of a properly oriented element.A bar with a circular cross section having two different diameters d and 2d is shown in the figure. The length of each segment of the bar is L/2T and the modulus of elasticity of the material is E. (a) Obtain a formula for the strain energy U of the bar due to the load P. (b) Calculate the strain energy if the load P = 27 kN, the length L = 600 mm, the diameter d = 40 mm, and the material is brass with E = 105 GPa.
- Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit. DATA FOR PROBLEM 2.7-5 Material Weight Density (lb/in3) Modulus of Elasticity (ksi) Proportional Limit (psi) Mild sleel 0.284 30,000 36,000 Tool steel 0.284 30,000 75,000 Aluminum 0.0984 10,500 60,000 Rubber (soft) 0.0405 0.300 300Solve the preceding problem if the cube is granite (E = 80 GPa, v = 0.25) with dimensions E = 89 mm and compressive strains E = 690 X l0-6 and = = 255 X 10-6. For part (c) of Problem 7.6-5. find the maximum value of cr when the change in volume must be limited to 0.11%. For part. find the required value of when the strain energy must be 33 J.A circular aluminum tube of length L = 600 mm is loaded in compression by forces P (see figure). The outside and inside diameters are d2= 75 mm and d1= 63 mm, respectively. A strain gage is placed on the outside of the lube to measure normal strains in the longitudinal direction. Assume that E = 73 GPa and Poissons ratio is v = 0.33. (a) IF the compressive stress in the tube is 57 MPa, what is the load P? (b) If the measured strain is e = 78 J X 10-6, what is the shortening
- A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?- 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?The statically indeterminate structure shown in the figure consists of a horizontal rigid bar AB supported by five equally spaced springs. Springs l, 2, and 3 have stiff nesses 3k, 5k. and k, respectively. When unstressed, the lower ends of all Five springs lie along: a horizontal line. Bar AB. which has weight W, causes the springs to elongate by an amount S. (a) Obtain a formula For the total strain energy of the springs in terms of the downward displacement d of the bar. (b) Obtain a formula for the displacement S by equating the strain energy of the springs to the work done by the weight W.