This problem represents an expansion of Example Problem 4.1, where the decking has an additional six feet to span and the beams are extended another bay. Loads on the structural system remain the same.
Determine the loads developed in each column support. Assume that columns are located at grids $1-A, \space 2-A,\space 3-A,\space 1-B, \space2-B,\space 3-B,\space 1-C, \space2-C, \space and \space 3-C.$

Question

This problem represents an expansion of Example Problem 4.1, where the decking has an additional six feet to span and the beams are extended another bay. Loads on the structural system remain the same.
Determine the loads developed in each column support. Assume that columns are located at grids [latex]1-A, \space 2-A,\space 3-A,\space 1-B, \space2-B,\space 3-B,\space 1-C, \space2-C, \space and \space 3-C.[/latex]

Accepted Answer

[latex] Deck \space DL[/latex] =[latex]8 \space psf [/latex]

[latex] Deck \space LL[/latex] =[latex]60 \space psf[/latex]

____________________________________________________

[latex] Total \space load[/latex] =[latex]68 \space psf[/latex]

Beam self-weight =[latex]10 \space \# /ft.[/latex]

Column self-weight =[latex]100 \space \# [/latex]

PLANK REACTION

[latex]\omega =68 \space \# /ft.^{2} (1 ^\prime )=68 \# /ft.[/latex]

BEAM REACTION First, analyze the planks that span six feet between grid lines [latex]A[/latex] and [latex]B[/latex].

[latex]R=\frac{\omega L}{2} =\frac{68 \# /ft.^{2}(6^\prime )}{2} =204\# [/latex] (Beam reaction)

Next, analyze the plank loads and beam support for the eight foot span between grids [latex]B[/latex] and [latex]C[/latex].

[latex]R=\frac{\omega L}{2} =\frac{68 \# /ft.^{2}(8^\prime )}{2} =272\# [/latex] (Beam reaction)

COLUMN REACTION All of the beam cases below represent uniformly loaded conditions with simply supported ends, which result in reactions that are [latex]R =\omega L/2[/latex]. The resulting reactions of the beams represent the loads present in each column.

First, analyze the beams along grid line [latex]A[/latex] :

Next, analyze the beams along grid line [latex]B[/latex] :

Then, analyze the beams along grid line [latex]C[/latex] :

COLUMN LOADS AND REACTIONS The perimeter columns along grid lines 1 and 3 receive half of the load of each beam. The interior columns along grid line 2 receive loads from two beams, which are added together to calculate the column loads.

Example Problem 4.2—Alternate Method

Another technique may be employed in determining the beam reactions without going through an analysis of the planks. This may be accomplished by evaluating the tributary widths of load for each beam and directly calculating the [latex]\omega[/latex] for each beam. For example, in the following figure, the tributary width of load assigned to the beams along grid line A is three feet. Therefore:

[latex] \omega =68 \space \# /ft.^{2} (3 ^\prime )+ 10\# /ft. =214 \# /ft. [/latex]

This [latex]\omega[/latex] value corresponds to the result obtained in the previous method.

And along grid line [latex]C[/latex], with tributary width = [latex]4^\prime[/latex] ,

[latex] \omega =68 \space \# /ft.^{2} (4 ^\prime )+ 10\# /ft. =282 \# /ft.\Longrightarrow [/latex] CHECKS

Similarly, for beams along gridline [latex]B[/latex]:

Tributary width [latex]=3^\prime+4^\prime=7^\prime[/latex]
[latex] herefore \omega =68 \space \# /ft.^{2} (7 ^\prime )+ 10\# /ft. =486 \# /ft.\Longrightarrow [/latex] CHECKS

Question 4.2: This problem represents an expansion of Example Problem 4.1,...

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