A cantilever beam with a 1 in diameter is loaded at the tip with a transverse force of 1000 lb. Figure 2.1 below shows the beam configuration and cross-section with points A at the top, point B at the center and point C at the midpoint between A and B.
a) Assume L = 10 in. For points A, B, and C sketch the three-dimensional stress elements labeling the coordinate directions and showing all stresses. Calculate the magnitudes of the stresses on each stress element, without neglecting transverse shear stress. And Finally calculate the maximum shear stress for each stress element.
b) For each element in part (a), calculate the maximum shear stress if the transverse shear stress is neglected. Determine the percent error for each stress element due to neglecting the transverse shear stress.
c) Repeat parts (a) and (b) for L = 4, 1, and 0,1 in. Compare the results and discuss what you can conclude from this analysis on the significance of transverse shear stress in combination with bending.