A W8 x 28 steel beam is loaded and supported as shown. Determine the maximum bending stress, and chose the right answer from the choices provided. The moment of inertia and the distance from the neutral axis to the extreme fiber are 98.0-in4 and 4.03-in, respectively. Note that all the values relevant to lengths given in the figure below are in feet. Picture10.jpg

Which of the following English phrases are logically equivalent to “P if and only if Q”? Select all that apply.

Determine the adequacy of a wood floor joist (2 x 10’s @ 16″ o.c.) supporting a dead load (DL) = 10 psf and live load (LL) = 40 psf. The length of each floor joist between supports is 14 feet. Assume that the allowable stresses for the Hem-Fir No. grade material are as follows: Fb = 1150 psi, Fv = 75 psi. The table of relevant properties is given below. To solve the problem, fill in the blanks of each solution step provide below. Where choices are provided, select the one closest to your calculated values. Solution Steps: A = [BLANK-1] in2 Sx = [BLANK-2] in3 Uniformly distributed load (UDL) on each floor joist = [BLANK-3] lb/ft length (chose your answer from these values: 33 or 67 or 100) Maximum shear force, Vmax = [BLANK-4] lb (chose your answer from these values: 469 or 700 or 234) Maximum bending moment, Mmax (note: pay attention to units) = [BLANK-5] ft-lb (chose your answer from these values: 3284 or 821 or 1624) Actual maximum shear stress, fv-max = [BLANK-6] psi (chose your answer from these values: 51 or 81 or 101) Is it adequate in shear? [BLANK-7] (yes or no) Actual maximum bending stress, fb-max = [BLANK-8] psi (chose your answer from these values: 1521 or 921 or 1221) Is it adequate in bending? [BLANK-9] (yes or no) Picture15.jpg

Beams are structural members designed to support [BLANK-1] (transverse or longitudinal) loads applied perpendicularly to their [BLANK-2] (transverse or longitudinal) axes.

The figure illustrates a simply supported beam with overhangs at both ends, including its loading, deflected shape, and a portion of the bending moment diagram. A vertical red line indicates a specific transverse section of the beam where the bending moment diagram crosses zero. At this section, the bending moment is zero, the sign of the bending moment changes, and the deflected shape transitions from concave to convex curvature (or vice versa). Such a section is known as the point of [BLANK-1]. Picture5.jpg

For a beam used as a structural member, its section modulus is the ratio between the moment of inertia of the beam cross-section and the distance from the neutral axis to the extreme fiber, top or bottom.

For the beam shown in the figure below, which surfaces/fibers will experience the maximum tensile and compressive bending stresses. Select the correct answer from the choices provided. Note that in the figure, the top part shows the transverse cross-section of the beam, while the bottom part shows the longitudinal cross-section along with the loading. Picture11.jpg

Presented below are the free-body diagram (FBD) of a loaded beam and the free-body diagram of the portion of the beam to the left of section cut G, located at a distance x from the left support. The internal shear force and bending moment at this section are denoted by VG and MG, respectively. Which set of equilibrium equations should be applied to correctly determine the values of VG and MG? Picture6.jpg

For elastic buckling of a slender column, PcrP_{cr} depends on: (Select all that apply)

The following are helpful equations and conversion facts that you may need for the exam. Refer to this as needed throughout the exam.