False We dont usually bother with sign conventions for V and Q. False To avoid misusing the shear formula, we must keep in mind that the edges of the cross section must be parallel to the y axis (so that the shear stresses act parallel to the y axis) True The maximum value of the shear stress occurs at the top or bottom of the beam where the first moment Q has its max value False The shear formula can only be used to determine the shear stress at the top and bottom of the cross section of a rectangular beam False The shear formula applies to prismatic and nonprismatic beams. True A beam of rectangular cross section whose height is twice as its width is less efficient in resisting bending than a circular beam that has the same area as the rectangular beam. A beam in this condition is called a beam of constant strength. True To minimize the amount of material and thereby have the lightest possible beam, we can vary the dimensions of the cross section so as to have the maximum allowable bending stress at very section. Fortunately, the flexure formula gives reasonably accurate values for bending stresses in nonprismatic beams whenever the changes in cross-sectional dimensions are gradual. However, nonprismatic beams are commonly used to reduce weight and improve appearance. True The beam theory described in ch 5 of the book was derived for prismatic beams. True The neutral axis passes through the centroid of the cross-sectional area when the material follows Hooke's law and there is no axial force acting on the cross section. True A positive bending moment produces positive curvature and a negative bending moment produces negative curvature. False Nonuniform bending refers to flexure in the presence of the shear forces, which means that the bending moments changes as we move along the axis of the beam. If the load in a beam is small, the beam will be nearly straight, the radius of curvature will be very small, and the curvature will be very large. Curvature is a measure of how sharply a beam is bent.
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