Data taken from a stressstrain test for a ceramic are given in the table.The curve is

Define homogeneous material.

Indicate the points on the stress-strain diagram which represent the proportional limit and the ultimate stress.

Define the modulus of elasticity E.

At room temperature, mild steel is a ductile material. True or false?

Engineering stress and strain are calculated using the actual cross-sectional area and length of the specimen. True or false?

As the temperature increases the modulus of elasticity will increase. True or false?

A 100-mm long rod has a diameter of 15 mm. If an axial tensile load of 100 kN is applied, determine its change is length, E = 200 GPa.

A bar has a length of 8 in. and cross-sectional area of \(12 \text { in }^{2}\). Determine the modulus of elasticity of the material if it is subjected to an axial tensile load of 10 kip and stretches 0.003 in. The material has linear-elastic behavior.

A 10-mm-diameter brass rod has a modulus of elasticity of E = 100 GPa. If it is 4 m long and subjected to an axial tensile load of 6 kN, determine its elongation.

The material for the 50-mm-long specimen has the stress–strain diagram shown. If P = 100 kN, determine the elongation of the specimen.

The material for the 50-mm-long specimen has the stress–strain diagram shown. If P = 150 kN is applied and then released, determine the permanent elongation of the specimen.

If the elongation of wire BC is 0.2 mm after the force P is applied, determine the magnitude of P. The wire is A-36 steel and has a diameter of 3 mm.

A concrete cylinder having a diameter of 6.00 in. and gauge length of 12 in. is tested in compression.The results of the test are reported in the table as load versus contraction. Draw the stress–strain diagram using scales of 1 in. = 0.5 ksi and \(1 \text { in. }=0.2\left(10^{-3}\right)\) in./in. From the diagram, determine approximately the modulus of elasticity.

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 rupture stress is \(\sigma_{r}=53.4\) ksi.

A tension test was performed on a specimen having an original diameter of 12.5 mm and a gauge length of 50 mm. The data are listed in the table. Plot the stress–strain diagram, and determine approximately the modulus of elasticity, the ultimate stress, and the fracture stress. Use a scale of 20 mm = 50 MPa and 20 mm = 0.05 mm/mm. Redraw the linear-elastic region, using the same stress scale but a strain scale of 20 mm = 0.001 mm/mm.

A tension test was performed on a steel specimen having an original diameter of 12.5 mm and gauge length of 50 mm. Using the data listed in the table, plot the stress–strain diagram, and determine approximately the modulus of toughness. Use a scale of 20 mm = 50 MPa and 20 mm = 0.05 mm/mm.

A specimen is originally 1 ft long, has a diameter of 0.5 in., and is subjected to a force of 500 lb. When the force is increased from 500 lb to 1800 lb, the specimen elongates 0.009 in. Determine the modulus of elasticity for the material if it remains linear elastic.

A structural member in a nuclear reactor is made of a zirconium alloy. If an axial load of 4 kip is to be supported by the member, determine its required cross-sectional area. Use a factor of safety of 3 relative to yielding. What is the load on the member if it is 3 ft long and its elongation is 0.02 in.? \(E_{\mathrm{zr}}=14\left(10^{3}\right) \mathrm{\ ksi}, \sigma_{Y}=57.5\) ksi. The material has elastic behavior.

The strut 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 the distributed load acts on the strut.

The \(\sigma-\epsilon\) diagram for a collagen fiber bundle from which a human tendon is composed is shown. If a segment of the Achilles tendon at A has a length of 6.5 in. and an approximate cross-sectional area of \(0.229 \mathrm{\ in}^{2}\) determine its elongation if the foot supports a load of 125 lb, which causes a tension in the tendon of 343.75 lb.

The stress–strain diagram for a metal alloy having an original diameter of 0.5 in. and a gauge 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 gauge length of 2 in. is given in the figure. If the specimen is loaded until it is stressed to 90 ksi, determine the approximate amount of elastic recovery and the increase in the gauge length after it is unloaded.

The stress–strain diagram for a steel alloy having an original diameter of 0.5 in. and a gauge 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 \(0.7 \mathrm{\ in}^{2}\) 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.

Determine the elongation of the square hollow bar when it is subjected to the axial force P = 100 kN. If this axial force is increased to P = 360 kN and released, find the permanent elongation of the bar. The bar is made of a metal alloy having a stress–strain diagram which can be approximated as shown.

A tension test was performed on an aluminum 2014-T6 alloy specimen. The resulting stress–strain diagram is shown in the figure. Estimate (a) the proportional limit, (b) the modulus of elasticity, and (c) the yield strength based on a 0.2% strain offset method.

A tension test was performed on an aluminum 2014- T6 alloy specimen. The resulting stress–strain diagram is shown in the figure. Estimate (a) the modulus of resilience; and (b) modulus of toughness.

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 \(\sigma\) 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 \(\sigma\) 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 \(\epsilon=0.12\) mm/mm.

The stress–strain diagram for a polyester resin is given in the figure. If the rigid beam is supported by a strut AB and post CD, both made from this material, and subjected to a load of P = 80 kN, determine the angle of tilt of the beam when the load is applied. The diameter of the strut is 40 mm and the diameter of the post is 80 mm.

The stress–strain diagram for a polyester resin is given in the figure. If the rigid beam is supported by a strut AB and post CD made from this material, determine the largest load P that can be applied to the beam before it ruptures. The diameter of the strut is 12 mm and the diameter of the post is 40 mm.

By adding plasticizers to polyvinyl chloride, it is possible to reduce its stiffness. The stress–strain diagrams for three types of this material showing this effect are given below. Specify the type that should be used in the manufacture of a rod having a length of 5 in. and a diameter of 2 in., that is required to support at least an axial load of 20 kip and also be able to stretch at most \(\frac{1}{4}\) in.

The stress–strain diagram for many metal alloys can be described analytically using the Ramberg-Osgood three parameter equation \(\epsilon=\sigma / E+k \sigma^{n}\) where E, k, and n are determined from measurements taken from the diagram. Using the stress–strain diagram shown in the figure, take \(E=30\left(10^{3}\right)\) ksi and determine the other two parameters k and n and thereby obtain an analytical expression for the curve.