Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 2.2, Problem 2.27P
The corners of the square plate are given the displacements indicated. Determine the average normal strains along side AB and diagonals AC and BD.
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The average normal strain and half the maximum in-planeshear strain is determined from the circle as the coordinates. True or false?
1. A loading causes the member to deform into the dashed shape. Explain how to
determine the normal strains ɛcd and ɛAB. The displacement A and the lettered
dimensions are known.
B
L.
L/2
A
2 L
(а)
L.
B
L/2
A
2 L
(b)
The state of plane strain on an element is represented by the following components:
Ex
=D340 x 10-6, ɛ, = , yxy
Ey
=D110 x 10-6,
3D180 x10-6
ху
Draw Mohr's circle to represent this state of strain.
Use Mohrs circle to obtain the principal strains and principal plane.
Chapter 2 Solutions
Mechanics of Materials (10th Edition)
Ch. 2.2 - A loading causes the member to deform into the...Ch. 2.2 - A loading causes the mamber to deform into the...Ch. 2.2 - A loading causes the wires to elongate into the...Ch. 2.2 - A loading causes the block to deform into the...Ch. 2.2 - A loading causes the block to deform into the...Ch. 2.2 - When force P is applied to the rigid arm ABC,...Ch. 2.2 - If the force P causes the rigid arm ABC to rotate...Ch. 2.2 - The rectangular plate is deformed into the shape...Ch. 2.2 - The triangular plate is deformed into the shape...Ch. 2.2 - The square plate is deformed into the shape shown...
Ch. 2.2 - The square deforms into the position shown by the...Ch. 2.2 - The pin-connected rigid rods AB and BC are...Ch. 2.2 - The wire AB is unstretched when = 45. If a load...Ch. 2.2 - If a horizontal load applied to the bar AC causes...Ch. 2.2 - Determine the shear strain xy at corners A and B...Ch. 2.2 - Determine the shear strain xy at corners D and C...Ch. 2.2 - The material distorts into the dashed position...Ch. 2.2 - The material distorts into the dashed position...Ch. 2.2 - Part of a control linkage for an airplane consists...Ch. 2.2 - Part of a control linkage for an airplane consists...Ch. 2.2 - The nylon cord has an original length L and is...Ch. 2.2 - A thin wire, lying along the x axis, is strained...Ch. 2.2 - Determine the shear strain xy at corners A and B...Ch. 2.2 - Determine the shear strain xy at corners D and C...Ch. 2.2 - Determine the average normal strain that occurs...Ch. 2.2 - The corners of the square plate are given the...Ch. 2.2 - The triangular plate is fixed at its base, and its...Ch. 2.2 - The triangular plate is fixed at its base, and its...Ch. 2.2 - The triangular plate is fixed at its base, and its...Ch. 2.2 - The polysulfone block is glued at its top and...Ch. 2.2 - The corners of the square plate are given the...Ch. 2.2 - The corners of the square plate are given the...Ch. 2.2 - The block is deformed into the position shown by...Ch. 2.2 - The rectangular plate is deformed into the shape...Ch. 2.2 - The rectangular plate is deformed into the shape...Ch. 2.2 - The nonuniform loading causes a normal strain in...Ch. 2.2 - The rectangular plate undergoes a deformation...Ch. 2.2 - The fiber AB has a length L and orientation . If...Ch. 2.2 - If the normal strain is defined in reference to...
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- 1. Find the relationships between strain components in the polar coordinate and strain components in the rectangular coordinate.arrow_forwardA loading causes the wires to elongate into the dashed shape. Explain how to determine the normal strain PAB in wire AB. The displacement Δ and the distances between all lettered points are known.arrow_forward1. The square plate is deformed as shown. Determine the normal and shear strains at E with respect to the X-Y and X’-Y’ axes. Hint: For normal strains find the changes in lengths of AB/CD, AC/BD, BC, and AD as a fraction of the original length. For shear strains, find the changes in the angles GEF and CED. 0.05" iD' Y' 8" A B B' 0.04" 8" 0.04"arrow_forward
- The piece of plastic is originally rectangular. Determine the average normal strain that occurs along the diagonals AC and DB. Determine the shear strain at corners A and B if the plastic distorts as shown by the dashed lines.arrow_forwardSolve it pleasearrow_forwardDetermine the shear strain Y., at corners A and B if the plastic distorts as shown by the dashed lines SOLUTION Geometry: Referring to the geometry shown in Fie a the small.anoto ancheir mins 3 mm 300 mm 4 mm 12 mm B mm 8 mm mmarrow_forward
- 4. Show that Cp = as +45°. principal strain and shear strainarrow_forwardA 45° strain rosette was placed on the surface of a critical point on an engineering part. The following were measured: Ea = 400 μ C ли 45° mm mm 45° ли Gauge a was aligned with the x-axis. a. Determine Ex, Ey, Yxy b. Using Mohr's Circle, find the principal strains and the maximum shear strain at that point, and find the orientation of the principal planes from the given x-y axes. y ли & = 450 μ ஆ b a mm X mm & c = 500 μ y+ ос mm mm eb 10₂ Xarrow_forwardFor the given state of plane strain, use Mohr's circle to determine the state of plane strain associated with axes x' and y rotated through the given angle 0. Ex = 0, Ɛy= +320µ, Yxy=-100µ, 0 = 25° (Round the final answers to one decimal place.) X The strains are Ex' = Ey'= Yx'y'=|arrow_forward
- For the state of a plane strain with Ex, Ey and yxy components: (a) construct Mohr's circle and (b) determine the equivalent in-plane strains for an element oriented at an angle of 30° clockwise. Ex = 250 x 10-6 Ey = 310 x 10-6 Yxy = -100 × 10-6arrow_forwardThe material distorts into the dashed position shown. Determine the average normal strains along with the diagonals AD and CF.arrow_forwardThe corners of the square plate are given the displacements indicated. Determine the average normal strains alongside AB and diagonals AC and BD.arrow_forward
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