Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 10.6, Problem 10.55P
To determine
To show that: The increase in the volume within the vessel is
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For the given plane strain state, use Mohr's circle to determine the strain state associated with the x' and y' axes rotated to θ indicated in the table:
\epsilon_x
\epsilon_y
\gamma_{xy}
θ
-500\mu
250\mu
120\mu
-15°
Consider a rectangular block of material of thickness h and sides 3b and 4b andhaving a triangular hole. If the material is subjected to the following displacement (where k is aconstant, use b=1, k =0.001):
Determine:(a) the strain matrix(b) the length of line BC after deformation,(c) the angle ABC after deformation.
Determine the transverse strain in the x axis of the solid subjected to longitudinal tension.
4 cm
1 cm
6x10³ N
2 cm
μ = 0,28
E=1,4x10" N/m²
6x10³ N
Chapter 10 Solutions
Mechanics of Materials (10th Edition)
Ch. 10.3 - Prove that the sum of the normal strains in...Ch. 10.3 - The state of strain at the point on the arm has...Ch. 10.3 - The state of strain at the point on the pin leaf...Ch. 10.3 - The state of strain at the point on the pin leaf...Ch. 10.3 - The state of strain at the point on the leaf of...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain- transformation equations to...
Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain on an...Ch. 10.3 - Determine the equivalent state of strain which...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain, which...Ch. 10.3 - Solve Prob.103 using Mohrs circle. 103. The state...Ch. 10.3 - using Mohrs circle. 103. The state of strain at...Ch. 10.3 - Solve Prob.105 using Mohrs circle. 105. The state...Ch. 10.3 - Solve Prob.108 using Mohrs circle 108. The state...Ch. 10.3 - using Mohrs circle. 106. The state of strain at a...Ch. 10.5 - The strain at point A on the bracket has...Ch. 10.5 - Determine (a) the principal strains at A, (b) the...Ch. 10.5 - Determine (a) the principal strains at A, in the...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained from each...Ch. 10.6 - For the case of plane stress, show that Hookes law...Ch. 10.6 - to develop the strain tranformation equations....Ch. 10.6 - Determine the modulus of elasticity and Polssons...Ch. 10.6 - If it is subjected to an axial load of 15 N such...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - A strain gage having a length of 20 mm Is attached...Ch. 10.6 - Determine the bulk modulus for each of the...Ch. 10.6 - The strain gage is placed on the surface of the...Ch. 10.6 - Determine the associated principal stresses at the...Ch. 10.6 - Determine the applied load P. What is the shear...Ch. 10.6 - If a load of P = 3 kip is applied to the A-36...Ch. 10.6 - The cube of aluminum is subjected to the three...Ch. 10.6 - The principal strains at a point on the aluminum...Ch. 10.6 - A uniform edge load of 500 lb/in. and 350 lb/in....Ch. 10.6 - Prob. 10.45PCh. 10.6 - A single strain gage, placed in the vertical plane...Ch. 10.6 - A single strain gage, placed in the vertical plane...Ch. 10.6 - If the material is graphite for which Eg = 800 ksi...Ch. 10.6 - Determine the normal stresses x and y in the plate...Ch. 10.6 - The steel shaft has a radius of 15 mm. Determine...Ch. 10.6 - Prob. 10.51PCh. 10.6 - The A-36 steel pipe is subjected to the axial...Ch. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Prob. 10.55PCh. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - Prob. 10.58PCh. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - The yield stress for a zirconium-magnesium alloy...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - If a machine part is made of tool L2 steel and a...Ch. 10.7 - Solve Prob.1063 using the maximum distortion...Ch. 10.7 - Prob. 10.65PCh. 10.7 - If a shaft is made of a material for which y = 75...Ch. 10.7 - Solve Prob.1066 using the maximum shear stress...Ch. 10.7 - If the material is machine steel having a yield...Ch. 10.7 - The short concrete cylinder having a diameter of...Ch. 10.7 - Prob. 10.70PCh. 10.7 - The plate is made of Tobin bronze, which yields at...Ch. 10.7 - The plate is made of Tobin bronze, which yields at...Ch. 10.7 - An aluminum alloy is to be used for a solid drive...Ch. 10.7 - If a machine part is made of titanium (TI-6A1-4V)...Ch. 10.7 - The components of plane stress at a critical point...Ch. 10.7 - The components of plane stress at a critical point...Ch. 10.7 - The 304-stainless-steel cylinder has an inner...Ch. 10.7 - The 304-stainless-steel cylinder has an inner...Ch. 10.7 - If the 2-in diameter shaft is made from brittle...Ch. 10.7 - If the 2-in diameter shaft is made from cast iron...Ch. 10.7 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - Prob. 10.82PCh. 10.7 - If the yield stress for steel is Y = 36 ksi,...Ch. 10.7 - Prob. 10.84PCh. 10.7 - The state of stress acting at a critical point on...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10.7 - Prob. 10.88PCh. 10.7 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - The gas tank is made from A-36 steel and has an...Ch. 10.7 - The internal loadings at a critical section along...Ch. 10.7 - If the material is machine steel having a yield...Ch. 10.7 - If the material is machine steel having a yield...Ch. 10 - In the case of plane stress, where the in-plane...Ch. 10 - The plate is made of material having a modulus of...Ch. 10 - If the material is machine steel having a yield...Ch. 10 - Determine if yielding has occurred on the basis of...Ch. 10 - The 60 strain rosette is mounted on a beam. The...Ch. 10 - Use the strain transformation equations to...Ch. 10 - If the strain gages a and b at points give...Ch. 10 - Use the strain-transformation equations and...Ch. 10 - Use the strain transformation equations to...Ch. 10 - Specify the orientation of the corresponding...
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- A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).arrow_forward- 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?arrow_forwardThe state of strain in a plane element is Ex = -300 x 10-6 , Ey= 450 x 10-6, and Yxy = 275 x 10-6. (a) Use the strain transformation equations to determine the equivalent strain components on an element oriented at an angle of 0 = 30° counterclockwise from the original position. (b) Sketch the deformed element due to these strains within the x-y plane.arrow_forward
- The Strain along the length direction of the block subjected to 3 mutually perpendicular forces as shown in figure is where E is Young's Modulus, pis Poisson's ratio Pz Px Py (-0,-µo,+µo) + μσ.) E y 7. E E (or -'or -*o) y 7, Earrow_forwardThree strain gauges are attached on the surface of the plane frame which is shown in Figure. The angle between each strain gauges are θº=63º. Reading from these gauges are: εa= 1100 μ, εb =335 μ and εc = -240 μCalculate:(a) The principal strains(b) The maximum shear strainarrow_forwardFor the state of a plane strain with εx, εy and γxy components: (a) construct Mohr’s circle and (b) determine the equivalent in-plane strains for an element oriented at an angle of 30° clockwise. εx = 255 × 10-6 εy = -320 × 10-6 γxy = -165 × 10-6arrow_forward
- 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)arrow_forwardThe strain value of the structure in the same direction as a result of the pull applied in the X axis from the bottom was measured as 0.26 mm / mm. Under the same loading condition: a) Calculate the strain on the Z axis of the structure. b) In this case, what is the strain type of the structure in the Z axis?arrow_forwardThe question is related to calculation of strain and is attached as an image.arrow_forward
- The normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression vy/3E where y = 2.3 lb/in.³ is the specific weight of the material, y = 0.8 in. is the distance from the free (i.e., bottom) end of the bar, L = 8 in. is the length of the bar, and E = 23000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar.arrow_forwardThe normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression vy/3E where y = 2.4 lb/in.³ is the specific weight of the material, y = 3.8 in. is the distance from the free (i.e., bottom) end of the bar, L = 19 in. is the length of the bar, and E= 24000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar. Part 1 Calculate the change in length of the bar due to its own weight. Answer: d = i x10-6 in.arrow_forward3arrow_forward
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