Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 3.4, Problem 3.2P
Data taken from a stress-strain test for a ceramic are given in the table. The curve is linear between the origin and the first point. Plot the diagram, and determine the modulus of elasticity and the modulus of resilience.
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Tensile test specimens are extracted from the "X" and "y" directions of a rolled sheet of metal. "x" is the rolling direction, "y" is
transverse to the rolling direction, and "z" is in the thickness direction. Both specimens were pulled to a longitudinal strain =
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Let’s consider a rod having a solid circular cross-section with diameter of 6 mm and it is made of a material having a Young’s modulus E = 200 Gpa and a Poisson’s ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 5.998 mm. determine the applied force F.
Remake the diagram for this problem. Empasize the area of 1,2,3, 4 and refer to the solution.
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Chapter 3 Solutions
Mechanics of Materials (10th Edition)
Ch. 3.4 - Define a homogeneous material.Ch. 3.4 - Indicate the points on the stress-strain diagram...Ch. 3.4 - Define the modulus of elasticity E.Ch. 3.4 - At room temperature, mild steel is a ductile...Ch. 3.4 - Engineering stress and strain are calculated using...Ch. 3.4 - As the temperature increases the modulus of...Ch. 3.4 - A 100-mm-long rod has a diameter of 15 mm. If an...Ch. 3.4 - A bar has a length of 8 in. and cross-sectional...Ch. 3.4 - A 10-mm-diameter rod has a modulus of elasticity...Ch. 3.4 - The material for the 50-mm-long specimen has the...
Ch. 3.4 - The material for the 50-mm-long specimen has the...Ch. 3.4 - If the elongation of wire BC is 0.2 mm after the...Ch. 3.4 - A tension test was performed on a steel specimen...Ch. 3.4 - Data taken from a stress-strain test for a ceramic...Ch. 3.4 - Data taken from a stress-strain test for a ceramic...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - The stress-strain diagram for a steel alloy having...Ch. 3.4 - The rigid beam is supported by a pin at C and an...Ch. 3.4 - The rigid beam is supported by a pin at C and an...Ch. 3.4 - Acetal plastic has a stress-strain diagram as...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - The stress-strain diagram for an aluminum alloy...Ch. 3.4 - A bar having a length of 5 in. and cross-sectional...Ch. 3.4 - The rigid pipe is supported by a pin at A and an...Ch. 3.4 - The rigid pipe is supported by a pin at A and an...Ch. 3.4 - Direct tension indicators are sometimes used...Ch. 3.4 - The rigid beam is supported by a pin at C and an...Ch. 3.4 - The rigid beam is supported by a pin at C and an...Ch. 3.4 - The stress-strain diagram for a bone is shown, and...Ch. 3.4 - The stress-strain diagram for a bone is shown and...Ch. 3.4 - The two bars are made of a material that has the...Ch. 3.4 - The two bars are made of a material that has the...Ch. 3.4 - The pole is supported by a pin at C and an A-36...Ch. 3.4 - The bar DA is rigid and is originally held in the...Ch. 3.7 - A 100-mm-long rod has a diameter of 15 mm. If an...Ch. 3.7 - A solid circular rod that is 600 mm long and 20 mm...Ch. 3.7 - A 20-mm-wide block is firmly bonded to rigid...Ch. 3.7 - A 20-mm-wide block is bonded to rigid plates at...Ch. 3.7 - The acrylic plastic rod is 200 mm long and 15 mm...Ch. 3.7 - The plug has a diameter of 30 mm and fits within a...Ch. 3.7 - The elastic portion of the stress-strain diagram...Ch. 3.7 - The elastic portion of the stress-strain diagram...Ch. 3.7 - The brake pads for a bicycle tire are made of...Ch. 3.7 - The lap joint is connected together using a 1.25...Ch. 3.7 - The lap joint is connected together using a 1.25...Ch. 3.7 - The rubber block is subjected to an elongation of...Ch. 3.7 - The shear stress-strain diagram for an alloy is...Ch. 3.7 - A shear spring is made from two blocks of rubber,...Ch. 3 - The elastic portion of the tension stress-strain...Ch. 3 - The elastic portion of the tension stress-strain...Ch. 3 - The rigid beam rests in the horizontal position on...Ch. 3 - The wires each have a diameter of 12 in., length...Ch. 3 - The wires each have a diameter of 12 in., length...Ch. 3 - diameter steel bolts. If the clamping force in...Ch. 3 - The stress-strain diagram for polyethylene, which...Ch. 3 - The pipe with two rigid caps attached to its ends...Ch. 3 - The 8-mm-diameter bolt is made of an aluminum...Ch. 3 - An acetal polymer block is fixed to the rigid...
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- Determine the stress resultants N(x), V(x), M(x) and draw the diagrams of the stress resultants and calculate the extremal values. At first, consider all parameters (F, a, L, ...) as variables and fill in their actual values at the end of your calculation.arrow_forwardNatural rubber is tested in tension to a maximum extension ratio of λ = 3. The Mooney-Rivlin constants for this material are found to be C1 = 0.069 MPa and C2 = 0.125 MPa. Plot the corresponding uniaxial stress vs. extension ratio behavior over the tested range. Derive an expression for the slope of the function, then determine the secant and tangent moduli at 100% strain.arrow_forwardYou must perform mechanical tests with a linear elastic material (the material follows Hooke's law) applying forces (tension) in the range 0 to Fmax/2 for Sample A and between 0 to Fmax for Sample B. The samples are made of same material but have different geometries (see illustration). (a) Which of the two samples receives the maximum stress (σmax)? (b) Which of the two samples will have the larger length change (ΔLmax)? (c) Plot the expected curves for the two samples in the force-length and stress-strain planes. (d) Clearly indicate the values that the variables force, length, stress, and strain take at the beginning and end of each curve.arrow_forward
- Let's consider a rod having a solid circular cross-section with diameter of 5 mm and it is made of a material having a Young's modulus E = 200 Gpa and a Poisson's ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 4.995 mm. determine the applied force F.arrow_forwardLet’s consider a rod having a solid circular cross-section with diameter of 6 mm and it is made of a material having a Young’s modulus E = 200 Gpa and a Poisson’s ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 5.998 mm. determine the applied force F. Select one: F = 6283 N F = 10472 N F = 4189 N F = 5236 N F = 13090 N F = 15708 Narrow_forwardLet's consider a rod having a solid circular cross-section with diameter of 4 mm and it is made of a material having a Young's modulus E = 200 Gpa and a Poisson's ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 3.995 mm. determine the applied force F. Select one: F = 10472 N O F = 6283N O F= 15708 N O F = 4189N O F = 5236 N O F = 13090 N Clear my choicearrow_forward
- The question is related to Modulus of rigidity and is attached as an image.arrow_forwardLet's consider a rod having a solid circular cross-section with diameter of 6 mm and it is made of a material having a Young's modulus E = 200 Gpa and a Poisson's ratio of 0.3. If a tensile force F is subjected to that rod cross- section, the diameter becomes 5.995 mm. determine the applied force F. Select one: F = 6283 N F = 4189 N F = 5236 N F = 10472 N F = 15708 N O F = 13090 Narrow_forwardLet's consider a rod having a solid circular cross- section with diameter of 4 mm and it is made of a material having a Young's modulus E = 120 Gpa and a Poisson's ratio of 0.33. If a tensile force F is subjected to that rod cross-section, the diameter becomes 3.995 mm. determine the applied force F. Select one: F = 3427 N F = 2856 N F = 5712 N F = 8568 N F = 7140 N F = 2285 Narrow_forward
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