Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Textbook Question
Chapter 2.2, Problem 2.34P
If the normal strain is defined in reference to the final length Δs′, that is,
Instead of in reference to the original length, Eq.2–2, show that the difference in these strains is represented as a second-order term, namely, ε − ε′ = εε′.
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Students have asked these similar questions
The 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 μrad
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.
The strain components Ex, Ey, and Yxy 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 0p, the
principal strain deformations, and the maximum in-plane shear strain distortion in a sketch.
Ex = 0 μE, Ey = 310 με, Yxy = 280 μrad. Enter the angle such that -45° ≤ 0,≤ +45°
Answer:
Ep1 =
Ep2 =
Ymax in-plane =
Yabsolute max. =
0p
=
με
με
urad
urad
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 state of strain at the point on the pin leaf has components of ϵx=200(10−6)ϵx=200(10−6) , ϵy=180(10−6)ϵy=180(10−6) , and γxy=−300(10−6)γxy=−300(10−6) . (Figure 1) -Use the strain transformation equations and determine the normal strain in the xx direction on an element oriented at an angle of θ=−55∘θ=−55∘ clockwise from the original position. -Determine the shear strain along the xy plain Determine the normal strain in the y direction.arrow_forwardThe deviatoric principal strains at a point in a loaded member are ₁, 2, 3. Show that ₁ + ₂ + 3 = 0 (ej)² + (e₂)² + (ez)² = [(e₁ = €₂)² + (€2 − €3)² + (€3 − €₁)²] -arrow_forwardThe state of strain in a plane element is ex =-200 x 10-6, Ey = 0, and yxy = 75 × 10-6 , as shown below. Determine the equivalent state of strain which represents (a) the principal strains (b) the maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original element. y Yxy 2 dy Yxy FExdx dxarrow_forward
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- The block is deformed into the position shown by the dashed lines. Determine the average normal strain along with line AB.arrow_forwardThe strain components ɛ, Ey, and yxy 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 0p, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex = 0 µE, ɛ, = 320 µɛ, Vxy = 240 µrad. Enter the angle suen that -45° s 0,s+45°.arrow_forwardDetermine the total strain (mm/mm) of a 2.70-m bar with a diameter of 21 mm subjected to a tensile force of 63 kN at a temperature increase of 77 C°. Consider the a=37.8 µm/mC° and E = 114 GPa.arrow_forward
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