Mechanics of Materials
11th Edition
ISBN: 9780137605514
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Textbook Question
Chapter 10.6, Problem 31P
to develop the strain tranformation equations. Eqs.10−5 and 10−6, from the stress tranformation equations, Eqs. 9−1 and 9−2.
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following table is the values of true stress - true strain of killed steel specimen with the dimensions shown in figure no. 1 below
A strain gauges system mounted at a point on a structural member that is subjected to multiaxial stress, where
we have the following readings:
Ex = 3.8 x104; &y = 5.5 x10-5; Ez = - 7.5 x10-5; Yy = 9.1 x104;
%3D
Determine the stress components if the member is made of an isotropic material with linear elastic behavior
having the following elastic properties:
Young's modulus E = 200 Gpa and Poisson's ratio v = 0.3;
Select one:
Ох %3D -100 Мра; оу %3D -50 Мра; о, %3D 30 Мра; Тху 3D 70 Мра;
Ox = -75 Mpa; o, = -50 Mpa; 0z = 40 Mpa; Ty = 80 Mpa3;
Oy = 300 Mpa; oy = -150 Mpa; 0z
3 100 Мра;B тyу
= 100 Mpa;
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Chapter 10 Solutions
Mechanics of Materials
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 leaf of...Ch. 10.3 - Use the strain transformation equations and...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. 10.5 - The strain at point A on the bracket has...
Ch. 10.5 - Determine (a) the principal strains at A, (b) the...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 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. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - Solve Prob.1063 using the maximum distortion...Ch. 10.7 - Prob. 70PCh. 10.7 - The plate is made of Tobin bronze, which yields at...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 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - Prob. 82PCh. 10.7 - If the yield stress for steel is Y = 36 ksi,...Ch. 10.7 - Prob. 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 - 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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- How can I solve for the %0.2 offset strain and the calculated stress? Original diameter : 6mm Original length : 30mm Fracture diameter : 4.54mmarrow_forwardE1= 0.0004 Q // The tensile tests were performed on longitudinal specimens of compact bone. The strain rosette is mounted on a bone were the 65° 50° readings are obtained for each gauge as shown in figure. Determine (a) the principal strains and (b) the shear strain and average normal strain. €2 = - 0.0005 65° €3 = 0.0003arrow_forwardQ1/ The table below shows the values of stress amplitude and life cycles : Fatigue strength Sf (Mpa) Number of cycles (Nf) 474 111 417 496 352 3002 316 7065 290 21930 262 66075 The test were done, to estimate the failure, on un-notched axially load specimens under zero mean stress. Calculate a and b using the stress -life equation.arrow_forward
- . In a uniaxial tension test, a dog-bone-shaped specimen is pulled in a machine. During the test, the force applied to the specimen, F, and the length of a gage section, L, are measured. The true stress, O,, and the true strain, &,, are defined by: 0₁ = F (KN) L (mm) FL EI. A Lo : &₁ = In # where A and Lo are the initial cross-sectional area and gage length, respectively. The true stress-strain curve in the region beyond yielding is often modeled by: o =KE The following are values of F and L measured in an experiment. Use the linearized form of the above equation determining the value of the coefficients K and m that best fit the data. The initial cross-sectional area and gage length are 4 = 1.25.10 m² and Lo=0.0125m. 24.6 29.3 31.5 33.3 34.8 35.7 36.6 37.5 38.8 39.6 40.4 12.58 12.82 12.91 12.95 13.05 13.21 13.35 13.49 14.08 14.21 14.48arrow_forwardFollowing experimental data are obtained from tensile test of a rectangular test specimen with original thickness of 2,5 mm, gauge width of 24 mm and gauge length of 101 mm: Load (N) Elongation (mm) 0 0 24372 0,183 23008 0,315 28357 5,777 35517 12,315 27555 17,978 23750 23,865 Based on the information above; draw stress-strain diagram of the material and answer the following questions. Question 1 ;Determine the elastic energy absorption capacity (in N.mm) of that specimen. Question 2; Determine the plastic energy absorption capacity (in N.mm) of that specimen.arrow_forwardThe strain of a component, which has a tensile modulus of 7 X 105 MPa, and subjected to a stress of 9000KPa, is a. 0.000026 b. 0.000129 c. 0.0026 d. 0.0000129arrow_forward
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