Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 8.4, Problem 19P
To determine
Find the yield strength for an offset of
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The bar has a cross-sectional area of 0.5 in2 and is made of a material that has a stress-strain diagram that can be approximated by the two line segments. Determine the elongation of the bar due to the applied loading.
The A-36 steel bar consists of two segments, one of a circular cross-section of radius r, and one of square cross-section. If the bar is subjected to the axial loading of P, determine the dimensions of the square segment so that the strain energy within the square segment is the same as in the circular segment.
*84 The stress-strain diagram for a metal alloy having an
original diameter of 12 mm and a gauge length of 50 mm is
given in the figure. Determine approximately the modulus of
elasticity for the material, the load on the specimen that causes
yielding, and the ultimate load the specimen will support.
a (MPa)
600
500
400
300
200
100
-e(mm/mm)
o 004 008 a12 0.16 0.20 024 0.28
O 0005 0.001 0.0015 0002 0.0025 0.003 0.0035
Chapter 8 Solutions
Statics and Mechanics of Materials (5th Edition)
Ch. 8.4 - Define a homogeneous material.Ch. 8.4 - Prob. 2FPCh. 8.4 - Prob. 3FPCh. 8.4 - Prob. 4FPCh. 8.4 - Prob. 5FPCh. 8.4 - As the temperature increases the modulus of...Ch. 8.4 - Prob. 7FPCh. 8.4 - Prob. 8FPCh. 8.4 - Prob. 9FPCh. 8.4 - Prob. 10FP
Ch. 8.4 - The material for the 50-mm-long specimen has the...Ch. 8.4 - If the elongation of wire BC is 0.2 mm after the...Ch. 8.4 - A tension test was performed on a steel specimen...Ch. 8.4 - Data taken from a stressstrain test for a ceramic...Ch. 8.4 - Data taken from a stressstrain test for a ceramic...Ch. 8.4 - Prob. 4PCh. 8.4 - The stress-strain diagram for a steel alloy having...Ch. 8.4 - Prob. 6PCh. 8.4 - The rigid beam is supported by a pin at C and an...Ch. 8.4 - The rigid beam is supported by a pin at C and an...Ch. 8.4 - Prob. 9PCh. 8.4 - The stressstrain diagram for an aluminum alloy...Ch. 8.4 - The stressstrain diagram for an aluminum alloy...Ch. 8.4 - Prob. 12PCh. 8.4 - A bar having a length of 5 in. and cross-sectional...Ch. 8.4 - The rigid pipe is supported by a pin at A and an...Ch. 8.4 - The rigid pipe is supported by a pin at A and an...Ch. 8.4 - Prob. 16PCh. 8.4 - The rigid beam is supported by a pin at C and an...Ch. 8.4 - Prob. 18PCh. 8.4 - Prob. 19PCh. 8.6 - A 100 mm long rod has a diameter of 15 mm. If an...Ch. 8.6 - A solid circular rod that is 600 mm long and 20 mm...Ch. 8.6 - Prob. 15FPCh. 8.6 - Prob. 16FPCh. 8.6 - The acrylic plastic rod is 200 mm long and 15 mm...Ch. 8.6 - The plug has a diameter of 30 mm and fits within a...Ch. 8.6 - The elastic portion of the stress-strain diagram...Ch. 8.6 - The elastic portion of the stress-strain diagram...Ch. 8.6 - The brake pads for a bicycle tire arc made of...Ch. 8.6 - The lap joint is connected together using a 1.25...Ch. 8.6 - The lap joint is connected together using a 1.25...Ch. 8.6 - Prob. 27PCh. 8.6 - The shear stress-strain diagram for an alloy is...Ch. 8.6 - Prob. 29PCh. 8 - The elastic portion of the tension stress-strain...Ch. 8 - Prob. 2RPCh. 8 - Prob. 3RPCh. 8 - Prob. 4RPCh. 8 - Prob. 5RPCh. 8 - Prob. 6RPCh. 8 - The stress-strain diagram for polyethylene, which...Ch. 8 - The pipe with two rigid caps attached to its ends...Ch. 8 - Prob. 9RPCh. 8 - Prob. 10RP
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- 8-21. The elastic portion of the stress-strain diagram for an aluminum alloy is shown in the figure. The specimen from which it was obtained has an original diameter of 12.7 mm and a gage length of 50.8 mm. When the applied load on the specimen is 50 kN, the diameter is 12.67494 mm. Determine Poisson's ratio for the material. (MPa) 490 (mm/mm) 0.007arrow_forwardThe brake pads for a bicycle tire are made of rubber. If a frictional force of 50 N is applied to each side of the tires, determine the average shear strain in the rubber. Each pad has cross-sectional dimensions of 20 mm and 50 mm.Gr = 0.20 MPa.arrow_forwardIf the normal strain is defined in reference to the final length Δs′, that is,P= = lim Δs′S 0 aΔs′ - Δs Δs′ b 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, P - P= = P P′.arrow_forward
- 5. The elastic portion of the stress-strain diagram for an aluminum alloy is shown in the figure on the right. The specimen from which it was obtained has an original diameter of 12.7 mm and a gage length of 50.8 mm. If a load of F = 60 kN is applied to the specimen, determine its new diameter and length, if v = 0.35. σ (MPa) 490 0.007 € (mm/mm)arrow_forwardQuestion 14 Determine the total strain (mm/mm) of a 2.58-m bar with a diameter of 23 mm subjected to a tensile force of 96 kN at a temperature increase of 60 C°. Consider the a=22.4 µm/mC° and E = 139 GPa. Express your answer to 5 decimal places.arrow_forwardThe normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression γy/3E where γ = 2.9 lb/in.3 is the specific weight of the material, y = 3.4 in. is the distance from the free (i.e., bottom) end of the bar, L = 17 in. is the length of the bar, and E = 24000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar.arrow_forward
- The rectangular plate is subjected to the deformation shown by the dashed line. Assume a - 575 mm, Ax- 1.8 mm, and Ay- 2.0 mm. Determine the shear strains Vxy and Yxy at point A. Answers: Vxy = Yxy" 7887 -006604 prad uradarrow_forwardA 75 mm long billet that has a 35 mm diameter is reduced to a diameter of 20 mm through direct extrusion. If o= 750 e025 MPa in the stress strain relationship for the wire material, determine the ram pressure.arrow_forwardThe rod is 200 mm long and 60 mm in diameter. If an axial load of 300 N is applied to it, determine the change in its length, the change in its diameter, normal stress and normal strain. The Poisson's ratio is 0.4 and the modulus of elasticity is 20 GPa.arrow_forward
- The stress-strain diagram for a bone is shown and can be described by the equation P = 0.45110-62 s + 0.36110-122 s3, where s is in kPa. Determine the modulus of toughness and the amount of elongation of a 200-mm-longregion just before it fractures if the failure occurs at P = 0.12 mm>mm.arrow_forwardThe elastic portion of the stress-strain diagram for an aluminum alloy is shown in the figure. The specimen from which it was obtained has an original diameter of 12.7 mm and a gage length of 50.8 mm. If a load of P=60 kN is applied to the specimen, determine its new diameter and length. Take v = 0.35. o (MPa) 490 e (mm/mm) 0.007arrow_forwardA tri-axial state of stress, σx , σy, and σz ,exists in a steel machine part. For steel, E = 200GPa and ν = 0.3. Determine the normal strain in the x-direction if σx = 100MPa, σy = 35MPa, σz = 70MPa. Determine the dilatation. Determine the modulus of rigidity.arrow_forward
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