ARCH 264/564 Structural Elements

Assignment #4r

Issued April 24, 2008.
Due: April 29, 2008 (not collected or graded)

Design the following beams/joists/girders for bending; then check for shear and deflection. Do not re-design if shear or deflection are not OK. Use L/360 criteria for deflection. Do not use live load reduction. Assume simple spans (i.e., hinge and roller constraints).

1. Wood joist and girder.
framing plan
Using Douglas Fir-Larch No. 2 dimension lumber, design joists at 16 inches o.c., and a girder (span = 6 feet). Assume that the girder load is distributed uniformly. Use L = 40 psf and D = 15 psf. Use C_H = 1.0.

2. Shear stress adjustment factor.
What shear stress adjustment factor, C_H, should be specified for a 6x12 girder subjected to a shear force of 6400#, if F'_v = 95 psi.

3. Steel beam and girder.
framing plan
Using A-992 steel, design the typical beam and cantilever girder shown in the sketches above, by selecting the lightest W-shape. Use L = 60 psf; and D = 50 psf. The girder is modeled, per load diagram, as a determinate cantilever beam with concentrated loads corresponding to the points where the beams frame in. Note that the load at the end of the cantilever is half that of the other loads (because its tributary area is half). Neglect the weight of the curtain wall; only include live and dead loads.

When checking girder deflection, model the cantilever girder as two separate beams, as shown below, in order to be able to use the available deflection tables. The "revised model" has moments and deflections close to that of the original model, as can be seen from the approximate deflected shapes sketched in the diagrams. Check deflection for both parts ("a" and "b"). Remember to use only the live load portion of the concentrated loads when checking deflection. Also, note that the span used in the calculation of allowable deflection is taken as 2 x L for the cantilever -- see note in Table A-8.1.
deflection model