The bar is made of an aluminum alloy having a stressstrain diagram that can be

The beam is made of an elastic plastic material for which \(\sigma_Y=250 \ \mathrm{MPa}\). Determine the residual stress in the beam at its top and bottom after the plastic moment \(\mathbf{M}_p\) is applied and then released.

The wide-flange member is made from an elastic-plastic material. Determine the shape factor.

Determine the shape factor for the cross section.

The beam is made of elastic perfectly plastic material. Determine the maximum elastic moment and the plastic moment that can be applied to the cross section. Take a = 2 in. and \(\sigma_Y = 36 \ \mathrm{ksi}\).

The box beam is made of an elastic perfectly plastic material for which \(\sigma_Y=250 \ \mathrm{MPa}\). Determine the residual stress in the top and bottom of the beam after the plastic moment \(\mathbf{M}_p\) is applied and then released.

Determine the shape factor for the wide-flange beam.

Determine the shape factor of the beam’s cross section.

The beam is made of elastic-perfectly plastic material. Determine the maximum elastic moment and the plastic moment that can be applied to the cross section. Take \(\sigma_Y = 36 \ \mathrm{ksi}\).

Determine the shape factor for the cross section of the H-beam.

The H-beam is made of an elastic-plastic material for which \(|sigma_Y=250 \ \mathrm{MPa}\) . Determine the residual stress in the top and bottom of the beam after the plastic moment \(\mathbf{M}_p\) is applied and then released.

Determine the shape factor of the cross section.

The beam is made of elastic-perfectly plastic material. Determine the maximum elastic moment and the plastic moment that can be applied to the cross section. Take \(\sigma_Y = 36 \ \mathrm{ksi}\).

Determine the shape factor of the cross section for the tube.

The beam is made from elastic-perfectly plastic material. Determine the shape factor for the thick-walled tube.

Determine the shape factor for the member.

The member is made from an elastic-plastic material. Determine the maximum elastic moment and the plastic moment that can be applied to the cross section. Take \(b = 4 \ \mathrm{in.}, h = 6 \ \mathrm{in.}, \sigma_Y = 36 \ \mathrm{ksi}\).

The beam is made of a material that can be assumed perfectly plastic in tension and elastic perfectly plastic in compression. Determine the maximum bending moment M that can be supported by the beam so that the compressive material at the outer edge starts to yield.

The box beam is made from an elastic-plastic material for which \(\sigma_Y=25 \ \mathrm{ksi}\) . Determine the intensity of the distributed load \(w_0\) that will cause the moment to be (a) the largest elastic moment and (b) the largest plastic moment.

The box beam is made from an elastic-plastic material for which \(\sigma_Y=36 \ \mathrm{ksi}\) . Determine the magnitude of each concentrated force \(\mathbf{P}\) that will cause the moment to be (a) the largest elastic moment and (b) the largest plastic moment.

The beam is made of a polyester that has the stress-strain curve shown. If the curve can be represented by the equation \(\sigma=\left[20 \ \tan ^{-1}(15 \epsilon)\right] \ \mathrm{ksi}\), where \(\tan ^{-1}(15 \epsilon)\) is in radians, determine the magnitude of the force \(\mathbf{P}\) that can be applied to the beam without causing the maximum strain in its fibers at the critical section to exceed \(\epsilon_{\max }=0.003 \ \mathrm{in./in}\).

The plexiglass bar has a stress–strain curve that can be approximated by the straight-line segments shown. Determine the largest moment M that can be applied to the bar before it fails.

The stress–strain diagram for a titanium alloy can be approximated by the two straight lines. If a strut made of this material is subjected to bending, determine the moment resisted by the strut if the maximum stress reaches a value of (a) \(\sigma_A\) and (b) \(\sigma_B\).

A beam is made from polypropylene plastic and has a stress–strain diagram that can be approximated by the curve shown. If the beam is subjected to a maximum tensile and compressive strain of \(\epsilon=0.02 \ \mathrm{mm/mm}\), determine the maximum moment M.

The beam has a rectangular cross section and is made of an elastic-plastic material having a stress–strain diagram as shown. Determine the magnitude of the moment \(\mathbf{M}\) that must be applied to the beam in order to create a maximum strain in its outer fibers of \(\epsilon_{\text {max}} = 0.008\).

The bar is made of an aluminum alloy having a stress–strain diagram that can be approximated by the straight line segments shown. Assuming that this diagram is the same for both tension and compression, determine the moment the bar will support if the maximum strain at the top and bottom fibers of the beam is \(\epsilon_{\text{max}} = 0.03\).