In the NCEES "Sample Questions + Solutions" book, the problems for the afternoon section are numbered 501 through 540. Today we are looking at Problem 504 of the Mechanical Systems section.
Description of Problem 504: A figure showing a 3D, statically indeterminate machine element is shown. The element is subject to combined loading. Several geometric dimensions (lengths, radii, height, etc) are provided. You are asked to list the dimensions that are needed to calculate the support reactions.
Analysis of Problem 504: At first, this problem might be somewhat intimidating because it is statically indeterminate and the geometry is three-dimensional. Nevertheless, you do not need to actually find the support reactions - only list the geometric dimensions that would need to be specified in order to find the support reactions. As always, this is actually easier than many strength of materials problems you had to do as undergraduate engineering student. Here is a similar problem we have created to test the same concept:
The post shown in the figure is fixed to to the floor at its base and has a diameter d. External loads P1 and P2 are acting in the x and y directions, respectively. Point A is located on the surface of the post within cross section a – a, which is at a distance h below the line of action of P1 . Distance b is from the axis of the vertical part of the post to the end of the horizontal part of the post.
Of the following statements, select the one that is true:
(A) The bending moment due to P1 causes a normal stress distribution at the cross section. At point A, the magnitude of this normal stress is independent of h.
(B) The shear force due to P1 causes a shear stress distribution at the cross section. At point A, this shear stress is highest.
(C) The load P2 causes a torsional stress at the cross section. At point A, this torsional stress is lowest.
(D) The bending moment due to P2 causes a normal stress distribution at the cross section. At point A, the magnitude of this normal stress is independent of h.
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