Determine the end reactions for beams B1, B2, B3, and B4. (Note, no credit will be given if you do not show your work. The reaction values given in the plan do not match my idealized numbers in every case.) (20 points total, 5 points each beam analysis) For each beam (B1, B2, B3, and B4) do the following:
1. Draw a beam load diagram. One end should be pinned and the other should show a roller. This is how a simply supported beam should be drawn.
2. Determine the tributary width (ft). (Recall: The tributary width is the combined lengths of / the distance to each adjacent beam.)
3. Use the tributary width to determine the total uniform linear load, WTL = WDL + WLL (plf). Tributary width x the area loads is the linear load carried by the beam however doesn’t forget to also include the beam's self-weight (plf) in the total linear load.
4. Determine the beam end reactions using R = (WTL)L/2 (lbs). This is the end support reactions at both ends of a uniformly loaded, simply supported beam. (Hint: You could determine these by using the equations of equilibrium (∑Mpt = 0, ∑Fy = 0 and ∑Fx = 0) however since there is symmetry in the loading and support conditions (both ends are pinned) the end reactions are the same, R = (WTL)L/2.)
5. Put a box around your end support reaction. Give correct magnitude, units and direction.
The floor system shown has a dead load (DL) that includes:
Floor tile and grout bedding = 17 psf
2VL120 (2″ deep metal deck with 4 72″ of concrete on top) = 45 psf
Mechanical ducts = 4 psf
Electrical = 1 psf
Gypsum board ceiling = 3 psf
Beam self-weight is given by its name (ie. W16x26 is 26 plf)
Girder self-weight is given by its name (ie. W30x90 is 90 plf)
The floor live load is 150 psf.
