A steel-framed floor for an office building was designed to support a load condition as follows:

Loads:

Live Load = 50 psf

Dead Loads:

Concrete = 150 $\# /ft.^{3}$

Steel decking = 5 psf

Mechanical equipment = 10 psf

Suspended ceiling = 5 psf

Steel beams = 25 #/ft.

Steel girders = 35 #/ft.

Using appropriate FBDs, determine the reaction forces for beams $B-1$ , $B-2$ , and $B-3$ and for girder $G-1$ .

Question

A steel-framed floor for an office building was designed to support a load condition as follows:

Loads:

Live Load = 50 psf

Dead Loads: Concrete = 150 [latex]\# /ft.^{3} [/latex]

Steel decking = 5 psf

Mechanical equipment = 10 psf

Suspended ceiling = 5 psf

Steel beams = 25 #/ft.

Steel girders = 35 #/ft.

Using appropriate FBDs, determine the reaction forces for beams [latex]B-1[/latex], [latex]B-2[/latex], and [latex]B-3[/latex] and for girder [latex]G-1[/latex].

Accepted Answer

Beam B-1:(Tributary width of load is [latex]6^\prime[/latex] )

[latex] \omega_{1} =120\space \# /ft.^{2} (6 ^\prime )+ 25\# /ft. =745 \# /ft. [/latex]

Beam B-2:(Tributary width of load is [latex]6^\prime + 6^\prime=12^\prime[/latex])

[latex] \omega_{2} =120\space \# /ft.^{2} (12 ^\prime )+ 25\# /ft. =1,465 \# /ft. [/latex]

Beam B-3: This beam has two different load conditions due to the changing tributary width created by the opening.

For 12 feet of span,

[latex] \omega_{3} =120\space \# /ft.^{2} (12 ^\prime )+ 25\# /ft. =1,465 \# /ft. [/latex]

For six feet of span,

[latex] \omega_{4} =120\space \# /ft.^{2} (6 ^\prime )+ 25\# /ft. =745 \# /ft. [/latex]

[latex]\left[\sum{M_{a}=0 } ight] -(745 \# /ft.)(8^{\prime} )(4^{\prime} )-(1,465 \# /ft.)(12^{\prime} )(14^{\prime} )+B_{y} (20^{\prime} )=0[/latex]

[latex] herefore B_{y}=13,498\# [/latex]

[latex]\left[\sum{F_{y}=0 } ight] -(745 \# /ft.)(8^{\prime} ) -(1465 \# /ft.)(12^{\prime} )+13,498\# +A_{y}=0[/latex]

[latex] herefore A_{y}=10,042\# [/latex]

Girder G-1: Girder [latex]G-1[/latex] supports reactions from beams [latex]B-2[/latex] and [latex]B-3[/latex]. Beam [latex]B-1[/latex] sends its reaction directly to the column and causes no load to appear in girder [latex]G-1[/latex].

[latex]\left[\sum{M_{a}=0 } ight] - 14,650 \# (12 ^{\prime} ) -13,498 \# (24^{\prime} )-(35\# /ft. imes 36^{\prime} )(18^{\prime} )+B_{y}(36^{\prime} )=0[/latex]

[latex] herefore B_{y}=14,512\# [/latex]

[latex]\left[\sum{F_{y}=0 } ight]-14,650 \# -13,498\# +14,512\# +A_{y}=0[/latex]

[latex] herefore A_{y}=14,896\# [/latex]

Question 4.3: A steel-framed floor for an office building was designed to ...

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