Determine the bending stress at point A of the beam, and the orientation of the neutral

Determine the bending stress developed at corners A and B.What is the orientation of the neutral axis?

Determine the maximum stress in the beam’s cross section.

The beam is subjected to a bending moment of \(M=20 \ \mathrm{kip} \cdot \mathrm{ft}\) directed as shown. Determine the maximum bending stress in the beam and the orientation of the neutral axis.

Determine the maximum magnitude of the bending moment \(\mathbf{M}\) that can be applied to the beam so that the bending stress in the member does not exceed 12 ksi.

If the resultant internal moment acting on the cross section of the aluminum strut has a magnitude of \(M=520 \ \mathrm{N} \cdot \mathrm{m}\) and is directed as shown, determine the bending stress at points A and B. The location \(\bar{y}\) of the centroid C of the strut’s cross-sectional area must be determined.Also, specify the orientation of the neutral axis.

The resultant internal moment acting on the cross section of the aluminum strut has a magnitude of \(M=520 \ \mathrm{N} \cdot \mathrm{m}\) and is directed as shown. Determine maximum bending stress in the strut. The location \(\bar{y}\) of the centroid C of the strut’s cross-sectional area must be determined.Also, specify the orientation of the neutral axis.

Consider the general case of a prismatic beam subjected to bending-moment components \(\mathbf{M}_y\) and \(\mathbf{M}_z\), as shown, when the x, y, z axes pass through the centroid of the cross section. If the material is linear-elastic, the normal stress in the beam is a linear function of position such that \(\sigma=a+b y+c z\). Using the equilibrium conditions \(0=\int_{\Lambda} \sigma d A, M_y=\int_A z \sigma d A, M_z=\int_A-y \sigma d A\), determine the constants a, b, and c, and show that the normal stress can be determined from the equation \(\sigma=\left[-\left(M_z I_y+M_y I_{y z}\right) y+\left(M_y I_z+M_z I_{y z}\right) z\right] /\left(I_y I_z-I_{y z}^2\right)\), where the moments and products of inertia are defined in Appendix A.

The cantilevered beam is made from the Z-section having the cross-section shown. If it supports the two loadings, determine the bending stress at the wall in the beam at point A. Use the result of Prob. 6–113.

The cantilevered beam is made from the Z-section having the cross-section shown. If it supports the two loadings, determine the bending stress at the wall in the beam at point B. Use the result of Prob. 6–113.

The cantilevered wide-flange steel beam is subjected to the concentrated force \(\mathbf{P}\) at its end. Determine the largest magnitude of this force so that the bending stress developed at A does not exceed \(\sigma_{\text{allow}}=180 \ \mathrm{MPa}\).

The cantilevered wide-flange steel beam is subjected to the concentrated force of P = 600 N at its end. Determine the maximum bending stress developed in the beam at section A.

If the beam is subjected to the internal moment of \(M=1200 \ \mathrm{kN} \cdot \mathrm{m}\) determine the maximum bending stress acting on the beam and the orientation of the neutral axis.

If the beam is made from a material having an allowable tensile and compressive stress of \((\sigma_{\text{allow}})_{t} =125 \ \mathrm{MPa}\) and \((\sigma_{\text{allow}})_{c} =150 \ \mathrm{MPa}\), respectively, determine the maximum allowable internal moment \(|mathbf{M}\) that can be applied to the beam.

The shaft is supported on two journal bearings at A and B which offer no resistance to axial loading. Determine the required diameter d of the shaft if the allowable bending stress for the material is \(\sigma_{\text{allow}} = 150 \ \mathrm{MPa}\).

The 30-mm-diameter shaft is subjected to the vertical and horizontal loadings of two pulleys as shown. It is supported on two journal bearings at A and B which offer no resistance to axial loading. Furthermore, the coupling to the motor at C can be assumed not to offer any support to the shaft. Determine the maximum bending stress developed in the shaft.

Using the techniques outlined in Appendix A, Example A.5 or A.6, the Z section has principal moments of inertia of \(I_y=0.060\left(10^{-3}\right) \ \mathrm{m}^4\) and \(I_z=0.471\left(10^{-3}\right) \ \mathrm{m}^4\), computed about the principal axes of inertia y and z, respectively. If the section is subjected to an internal moment of \(M=250 \ \mathrm{~N} \cdot \mathrm{m}\) directed horizontally as shown, determine the stress produced at point A. Solve the problem using Eq. 6-17.

Solve Prob. 6–122 using the equation developed in Prob. 6–113.

Using the techniques outlined in Appendix A, Example A.5 or A.6, the Z section has principal moments of inertia of \(I_y=0.060\left(10^{-3}\right) \ \mathrm{m}^4\) and \(I_z=0.471\left(10^{-3}\right) \ \mathrm{m}^4\), computed about the principal axes of inertia y and z, respectively. If the section is subjected to an internal moment of \(M=250 \ \mathrm{~N} \cdot \mathrm{m}\) directed horizontally as shown, determine the stress produced at point B. Solve the problem using Eq. 6-17.

Determine the bending stress at point A of the beam, and the orientation of the neutral axis. Using the method in Appendix A, the principal moments of inertia of the cross section are \(I_z^{\prime}=8.828 \ \mathrm{in}^4\) and \(I_y^{\prime}=2.295 \ \mathrm{in}^4\), where \(z^{\prime}\) and \(y^{\prime}\) are the principal axes. Solve the problem using Eq. 6-17.

Determine the bending stress at point A of the beam using the result obtained in Prob. 6-113. The moments of inertia of the cross sectional area about the z and y axes are \(I_z=I_y=5.561 \ \mathrm{in}^4\) and the product of inertia of the cross sectional area with respect to the z and y axes is \(I_{y z}=-3.267 \ \mathrm{in}^4\). (See Appendix A)