Question

The plan view of a typical floor of a four-story heavy storage facility is shown below. The floor and roof live load is 250 psf, and the dead load on all foors and the roof consists of the structure self-weight plus 10 psf for utilities. W 12:96 beams are spaced at 12 ft; w 18x106 reinforced one-way concrete floor/roof slab is 8" thick, each story is 12' high, and the reinforced concrete columns have a 14" x 14" cross-section girders are spaced at 27 ft. The A) Determine the maximum bending moment in a typical interior and exterior beam B) Determine the maximum bending moment in a typicl interior and exterior girder. C) Determine the largest axial force in a typical interior column. W 18x106 W 12x96 3 @ 12 36 4@36. 144.

Answer 1

A)

Slab thickness=8"

Self weighy of slab=(8/12)*150=100 psf

Super dead Load=10 psf

Live load=250 psf

Factored area load on floor=1.2*(100+10)+1.6*250=532 psf

Tributtary width of typical interior beam=12 ft

Span of typical interior beam=27 ft

Factored load beam from floor=12*532/1000=6.384 kip/ft

Factored weight of beam=1.2*96/1000=0.1152 kip/ft

Total factored iniform load on beam=6.384+0.1152=6.5 kip/ft

Maximum moment in typical interior beam=6.5*27²/8=592.3 kip-ft

Tributray width of typical exterior beam=6 ft

Factored uniform load from floor=6*532/1000=3.192 kip/ft

Total factored load=3.192+0.1152=3.31 kip/ft

Maximum moment in typical exterior beam=3.31*27²/8=301.6 kip-ft

B)

Girders are basically supporting beams in addition to their own weight

For typical interior girder, load is coming from both sides

Factored load on interior girder from each beam=6.5*27/2=87.75 kips

Span of each girder=36 ft

Factired moment in girder due to loads from beams=2*87.75*12=2106 kip-ft

Facored momeent in girder due to its own weight=1.2*0.106*36²/8=21 kip-ft

Total moment in interior girder=2106+21=2127 kip-ft

Typical exterior girder has loads from beams only from one side

Factored moment in girder due to loads from beam=87.75*12=1053 kip-ft

Factored moment in gorder due to its onw weight=21 kip-ft

Total momemt in girder=1053+21=1074 kip-ft

C)

Maximim axial load will be in an interior column since that has maximum tributray area

Tributry area of interir colimn=36*27=972 ft²

Factored load on column from floor=972*532/1000=517 kips

Factored load on column from beam weight=1.2*96*27/1000=3.11 kips

Factored lpad on column from girder weight=1.2*106*36/1000=4.58 kips

Total axial.load=517+3.11+4.58=524.7 kips