Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Chapter 2.2, Problem 2.3PP
A loading causes the wires to elongate into the dashed shape. Explain how to determine the normal strain εAB in wire AB. The displacement Δ and the distances between all lettered points are known.
P2–3
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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?
(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
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
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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- A thin wire, lying along the x axis, is strained such that each point on the wire is displaced Δx = kx2 along the x axis. If k is constant, what is the normal strain at any point P along the wire?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_forwardThe ratio of linear strain to the lateral strain is called shear strain. Select one: True Falsearrow_forward
- 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 Narrow_forwardThe 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_forward5 decimal places Determine the total strain (mm/mm) of a 2.64-m bar with a diameter of 21 mm subjected to a tensile force of 71 kN at a temperature increase of 49 C°. Consider the α=27.3 µm/mC° and E = 122 GPa.arrow_forward
- Your answer is partially correct. The strain components for a point in a body subjected to plane strain are ɛ, = -890 µɛ, ɛ, = -690µɛ and yy = -682 prad. Using Mohr's circle, determine the principal strains (ɛp1 > Ep2), the maximum inplane shear strain yip, and the absolute maximum shear strain ymax at the point. Show the angle 0, (counterclockwise is positive, clockwise is negative), the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Answers: Ep1 = 927.99 με. Ep2 = 1116.0 PE. Vip = 188.01 prad. Ymax = -188.01 prad. Op = 36.82arrow_forwardIf a rubber material is deformed as shown in the following figure, determine the normal strain diagonal AC. 10 mm 2 mm 1 mm 10 mm Barrow_forwardIf a rubber material is deformed as shown in the following figure, determine the normal strain along diagonal AC. 2 mm 3 mm 20 mm A B 20 mm Select one: O 0.1281 O 0.0607 O 0.1402 O 0.0853 O 0.0326arrow_forward
- If a rubber material is deformed as shown in the following figure, determine the normal strain along diagonal BD. D C 4 mm 2 mm 10 mm A 10 mm Select one: O 0.0607 O 0.0382 1020 DAarrow_forwardThe strain components at a point in a body subjected to plane strain are & 850μ, Ey -300μ, and Yay 400μ. Determine the principal strains and the maximum shearing strain at the point. Show the principal strain deformations and the maximum shearing strain distortion on a sketch. = = =arrow_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
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