A two-story office building has interior columns that are spaced 22 ft apart in two perpendicular directions. If the (flat) roof loading is 20 lb/ft^2 ,determine the reduced live load supported by a typical interior column located at ground level.

Question

A two-story office building has interior columns that are spaced 22 ft apart in two perpendicular directions. If the (flat) roof loading is [latex]20{lb}/{ft^{2} } [/latex],determine the reduced live load supported by a typical interior column located at ground level.

Accepted Answer

As shown in Fig. 1–9, each interior column has a tributary area or effective loaded area of [latex] A_{T}=\left(22 ft\right) \left(22 ft\right) =48 ft^{2} [/latex] A ground-floor column therefore supports a roof live load of

[latex] F_{R}= \left(20 {lb}/{ft^{2} }\right) \left(484 ft^{2} \right) =9680 lb =9.68 k[/latex]

This load cannot be reduced, since it is not a floor load. For the second floor, the live load is taken from Table 1–4:

TABLE 1-4 . Minimum Live Loads
Live Load			Live Load
Occupancy or Use	psf	[latex]{kN}/{m^{2}}[/latex]	Occupancy or Use	psf	[latex]{kN}/{m^{2}}[/latex]
Assembly areas and theaters			Residential
Fixed seats	60	2.87	Dwellings (one- and two-family)	40	1.92
Movable seats	100	4.79	Hotels and multifamily houses
Dance halls and ballrooms	100	4.79	Private rooms and corridors	40	1.92
Garages (passenger cars only)	50	2.40	Public rooms and corridors	100	4.79
Office buildings			Schools
Lobbies	100	4.79	Classrooms	40	1.92
Offices	50	2.40	Corridors above first floor	80	3.83
Storage warehouse
Light	125	6.00
Heavy	250	11.97

[latex]L_{0}=50 {lb}/{ft^{2} } [/latex] Since [latex]K_{LL}=4 [/latex] ,then [latex] 4A_{T}=4\left(484 ft^{2} \right) =1936 ft^{2}[/latex] and [latex]1936 ft^{2} \gt 400 ft^{2} [/latex], the live load can be reduced using Eq. 1–1. Thus,

[latex]L=L_{0} \left(0.25+\frac{15}{\sqrt{K_{LL}A_{T} } } \right) [/latex] (FPS units)

[latex]L=L_{0} \left(0.25+\frac{4.57}{\sqrt{K_{LL}A_{T} } } \right) [/latex] (SI units)

[latex] L=50 \left(0.25+\frac{15}{\sqrt{1936 } } \right)=29.55 {lb}/{ft^{2}} [/latex]

The load reduction here is [latex]\left(29.55/50\right) 100 \%=59.1 \% \gt 50\% [/latex] O.K.

Therefore

[latex] F_{F}=\left(29.55{lb}/{ft^{2}}\right) \left(484 ft^{2} \right)=14 300 lb=14.3k [/latex]

The total live load supported by the ground-floor column is thus

[latex]F=F_{R}+F_{F}=9.68k+14.3k=24.0 k [/latex]

Question 1.2: A two-story office building has interior columns that are sp...

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