Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Textbook Question
Chapter 2.2, Problem 2.4PP
A loading causes the block to deform into the dashed shape. Explain how to determine the strains εAB εAC, εBC, (γA)xy. The angles and distances between all lettered points are known.
P2–4
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Students have asked these similar questions
The ratio of longitudinal strain to the lateral strain of the object is known as Poisson's ratio
Select one:
O True
O False
Determine the average normal strain along diagonal DB, based on the original plate (blue) and the deformed shaped (dashed line):
2 mm
y
C
300 mm
12 mm
D
-400 mm
A
5 mm
B
3 mm
4 mm
12 mm
X
(a) Determine the shear strain at corner A if the plate distorts as
shown by the dashed line.
(b) Determine the average normal strain that occurs along the
diagonal AC and DB.
5 mm
2 mm
4 mm
2 mm
IB
300 mm
$2 mm
D
A
400 mm
3 mm
Chapter 2 Solutions
Mechanics of Materials
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 - Prob. 2.1PCh. 2.2 - Prob. 2.2PCh. 2.2 - Prob. 2.3PCh. 2.2 - Prob. 2.4PCh. 2.2 - Prob. 2.5PCh. 2.2 - Prob. 2.6PCh. 2.2 - The pin-connected rigid rods AB and BC are...Ch. 2.2 - Prob. 2.8PCh. 2.2 - Prob. 2.9PCh. 2.2 - Prob. 2.10PCh. 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 - Prob. 2.13PCh. 2.2 - Prob. 2.14PCh. 2.2 - Prob. 2.15PCh. 2.2 - Prob. 2.16PCh. 2.2 - Prob. 2.17PCh. 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 - Prob. 2.21PCh. 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 - Prob. 2.25PCh. 2.2 - Prob. 2.26PCh. 2.2 - Prob. 2.27PCh. 2.2 - Prob. 2.28PCh. 2.2 - The rectangular plate is deformed into the shape...Ch. 2.2 - The rectangular plate is deformed into the shape...Ch. 2.2 - Prob. 2.31PCh. 2.2 - Prob. 2.32PCh. 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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- The average normal strain and half the maximum in-planeshear strain is determined from the circle as the coordinates. True or false?arrow_forwardP2-4. A loading causes the block to deform into the dashed shape. Explain how to determine the strains eAR, EAC, EBC. (YA)zy- The angles and distances between all lettered points are known. B C B' 7C A D P2-4arrow_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
- The ratio of linear strain to the lateral strain is called shear strain. Select one: True Falsearrow_forward1. 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)arrow_forwardIn its undeformed state the assembly is represented by A-B-C-D, with theta = 0.53 in radians. The deformed shape is: A’-B’-C’-D. The deformation is such that the normal strain in AB is: ϵAB = 0.033 and that in CB is: ϵCB=0.031. Calculate the normal strain in BD (correctly up to four decimal places) neglecting the higher-order contributions due to the normal strains in AB and CB.arrow_forward
- 2-23. The rectangular plate is subjected to the deformation shown by the dashed lines. Determine the average shear strain yxy of the plate. *2-24. The rectangular plate is subjected to the deformation shown by the dashed lines. Determine the average normal strains along the diagonal AC and side AB. B C 150 mm 4 3 mm -3 mm -200 mm- Probs. 2-23/24arrow_forward! Required information Consider the given state of plane strain. Ex=-180µ, Ey=-260µ, Yxy=+295µ Use Mohr's circle to determine the orientation and magnitude of the principal strains. (Round the final answers to one decimal place.) The orientations are %3D The magnitudes are Ea 93arrow_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 8. Ex=-500μ, &y=+250µ, Yxy = 0, 0 = 13° O (Round the final answers to one decimal place.) The strains are Ex'= Ey₁ = | Vx'y¹=[ Harrow_forward
- ! Required information Consider the given state of plane strain. Ex =-180µ, Ey=-260µ, Yxy= +295µ Use Mohr's circle to determine the orientation and magnitude of the principal strains. (Round the final answers to one decimal place.) The orientations are The magnitudes are Ea Ebarrow_forwardThe strain components e x, e y, and γ xy are given for a point in a body subjected to plane strain. Using Mohr’s circle, determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle θ p, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex Ey Yxy −1,570 με -430με -950 μradarrow_forwardThe plate is deformed into the dashed shape shown in Fig. 2-6a. If in this deformed shape horizontal lines on the plate remain horizontal and do not change their length, determine (a) the average normal strain along the side AB, and (b) the average shear strain in the plate relative to the x and y axes.arrow_forward
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