Solution: The stressstrain diagram for a steel alloy having

A tension test was performed on a steel specimen having an original diameter of 0.503 in. and gage length of 2.00 in. The data is listed in the table. Plot the stress–strain diagram and determine approximately the modulus of elasticity, the yield stress, the ultimate stress, and the fracture stress. Use a scale of 1 in. = 20 ksi and 1 in. = 0.05 in./in. Redraw the elastic region, using the same stress scale but a strain scale of 1 in. = 0.001 in./in.

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.

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 approximately the modulus of toughness. The fracture stress is \(\sigma_{f}=53.4 \mathrm{ksi}\).

The stress–strain diagram for a steel alloy having an original diameter of 0.5 in. and a gage length of 2 in. 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.

The stress–strain diagram for a steel alloy having an original diameter of 0.5 in. and a gage length of 2 in. is given in the figure. If the specimen is loaded until it is stressed to 70 ksi, determine the approximate amount of elastic recovery and the increase in the gage length after it is unloaded.

The stress–strain diagram for a steel alloy having an original diameter of 0.5 in. and a gage length of 2 in. is given in the figure. Determine approximately the modulus of resilience and the modulus of toughness for the material.

The rigid beam is supported by a pin at C and an A-36 steel guy wire AB. If the wire has a diameter of 0.2 in., determine how much it stretches when a distributed load of w = 100 lb/ft acts on the beam. The material remains elastic.

The rigid beam is supported by a pin at C and an A-36 steel guy wire AB. If the wire has a diameter of 0.2 in., determine the distributed load w if the end B is displaced 0.75 in. downward.

Acetal plastic has a stress-strain diagram as shown. If a bar of this material has a length of 3 ft and cross-sectional area of \(0.875 \mathrm{in}^{2}\), and is subjected to an axial load of 2.5 kip, determine its elongation.

The stress–strain diagram for an aluminum alloy specimen having an original diameter of 0.5 in. and a gage length of 2 in. is given in the figure. Determine approximately 3 the modulus of elasticity for the material, the load on the specimen that causes yielding, and the ultimate load the specimen will support.

The stress–strain diagram for an aluminum alloy specimen having an original diameter of 0.5 in. and a gage length of 2 in. is given in the figure. If the specimen is loaded until it is stressed to 60 ksi, determine the approximate amount of elastic recovery and the increase in the gage length after it is unloaded.

The stress–strain diagram for an aluminum alloy specimen having an original diameter of 0.5 in. and a gage length of 2 in. is given in the figure. Determine approximately the modulus of resilience and the modulus of toughness for the material.

A bar having a length of 5 in. and cross-sectional area of \(0.7 \text { in. }^{2}\) is subjected to an axial force of 8000 lb. If the bar stretches 0.002 in., determine the modulus of elasticity of the material. The material has linear elastic behavior.

The rigid pipe is supported by a pin at A and an A-36 steel guy wire BD. If the wire has a diameter of 0.25 in., determine how much it stretches when a load of P = 600 lb acts on the pipe.

The rigid pipe is supported by a pin at A and an A-36 guy wire BD. If the wire has a diameter of 0.25 in., determine the load P if the end C is displaced 0.075 in. downward.

Direct tension indicators are sometimes used instead of torque wrenches to ensure that a bolt has a prescribed tension when used for connections. If a nut on the bolt is tightened so that the six 3-mm high heads of the indicator are strained 0.1 mm/mm, and leave a contact area on each head of \(1.5 \text { mm }^{2}\), determine the tension in the bolt shank. The material has the stress–strain diagram shown.

The rigid beam is supported by a pin at C and an A992 steel guy wire AB of length 6 ft. If the wire has a diameter of 0.2 in., determine how much it stretches when a distributed load of w = 200 lb/ft acts on the beam. The wire remains elastic.

The rigid beam is supported by a pin at C and an A992 steel guy wire AB of length 6 ft. If the wire has a diameter of 0.2 in., determine the distributed load w if the end B is displaced 0.12 in. downward. The wire remains elastic.

The stress–strain diagram for a bone is shown, and can be described by the equation \(\epsilon=0.45\left(10^{-6}\right) \sigma+\) \(0.36\left(10^{-12}\right) \sigma^{3}\), where s is in kPa. Determine the yield strength assuming a 0.3% offset.

The stress–strain diagram for a bone is shown and can be described by the equation \(\epsilon=0.45\left(10^{-6}\right) \sigma+\) \(0.36\left(10^{-12}\right) \sigma^{3}\), where s is in kPa. Determine the modulus of toughness and the amount of elongation of a 200-mm-long region just before it fractures if failure occurs at \(\epsilon=0.12 \mathrm{~mm} / \mathrm{mm}\).

The two bars are made of a material that has the stress–strain diagram shown. If the cross-sectional area of bar AB is \(1.5 \mathrm{in}^{2} \text { and } B C \text { is } 4 \mathrm{in}^{2}\), determine the largest force P that can be supported before any member fractures. Assume that buckling does not occur.

The two bars are made of a material that has the stress–strain diagram shown. Determine the cross-sectional area of each bar so that the bars fracture simultaneously when the load P = 3 kip. Assume that buckling does not occur.

The pole is supported by a pin at C and an A-36 steel guy wire AB. If the wire has a diameter of 0.2 in., determine how much it stretches when a horizontal force of 2.5 kip acts on the pole.

The bar DA is rigid and is originally held in the horizontal position when the weight W is supported from C. If the weight causes B to displace downward 0.025 in., determine the strain in wires DE and BC. Also, if the wires are made of A-36 steel and have a cross-sectional area of \(0.002 \mathrm{in}^{2}\), determine the weight W.

The acrylic plastic rod is 200 mm long and 15 mm in diameter. If an axial load of 300 N is applied to it, determine the change in its length and the change in its diameter. \(E_{\mathrm{p}}=2.70 \mathrm{GPa}, \nu_{\mathrm{p}}=0.4\).

The plug has a diameter of 30 mm and fits within a rigid sleeve having an inner diameter of 32 mm. Both the plug and the sleeve are 50 mm long. Determine the axial pressure p that must be applied to the top of the plug to cause it to contact the sides of the sleeve. Also, how far must the plug be compressed downward in order to do this? The plug is made from a material for which E = 5 MPa, \(\nu=0.45\).

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.

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 andagagelengthof50.8mm.IfaloadofP=60kNisapplied to the specimen, determine its new diameter and length. Take \(\nu=0.35\).

The 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. \(G_{\mathrm{r}}=0.20 \mathrm{MPa}\).

The lap joint is connected together using a 1.25 in. diameter bolt. If the bolt is made from a material having a shear stress–strain diagram that is approximated as shown, determine the shear strain developed in the shear plane of the bolt when P = 75 kip.

The lap joint is connected together using a 1.25 in. diameter bolt. If the bolt is made from a material having a shear stress–strain diagram that is approximated as shown, determine the permanent shear strain in the shear plane of the bolt when the applied force P = 150 kip is removed.

The rubber block is subjected to an elongation of 0.03 in. along the x axis, and its vertical faces are given a tilt so that \(\theta=89.3^{\circ}\). Determine the strains \(\epsilon_{x}, \epsilon_{y} \text { and } \gamma_{x y}\). Take \(??\nu_{\mathrm{r}}=0.5\).

The shear stress–strain diagram for an alloy is shown in the figure. If a bolt having a diameter of 0.25 in. is made of this material and used in the lap joint, determine the modulus of elasticity E and the force P required to cause the material to yield. Take \(\nu=0.0.3\).

A shear spring is made from two blocks of rubber, each having a height h, width b, and thickness a. The blocks are bonded to three plates as shown. If the plates are rigid and the shear modulus of the rubber is G, determine the displacement of plate A when the vertical load P is applied. Assume that the displacement is small so that \(\delta=a \tan \gamma \approx a \gamma\).