Loading

David Wagner 2007/12/03 12:24

”…several rest areas on a major road from San Antonio to McAllen, Texas.”

The loading is calculated for LRFD analysis.

Assume the overhangs are at least 3' on every side, rounded up to a whole number of 4×8 plywood sheets.

  • The roof is 45.2×30.2 in plan, nominally 48'x31' a horizontal plane area of 1490 sf.
  • The roof slopes 6' over 24' (3-in-12 or 14°), a length of 31.1'. The inclined area is nominally 48×32', 1536 sf.

Dead Loads

Note the relatively small weights of the glulam roof beams are addressed in the design and analysis sections.

Roofing (14-gage Steel)3.3 psf
¾” Plywood (¾x3 psf/in)2.25
2×10 @ 16”6
Loose Insulation, (8×0.5 psf/in)4.0
Acoustical Tiles1.0
Roof Inclined Dead Load D16.55 psf

With the roof slope taken conservatively as 15°, the horizontal plane roof dead load is 16.55/cos(15) = 17.1 psf.

Roof Horizontal Plane Dead Load D17.1 psf

Roof Live Load

Ordinary Roof Live Load Lr20 psf

–Table 1607.1, IBC 2006

Snow Load

The design ground snow load, pg, ranges from zero to 5 psf in the area of interest. [2006 IBC, Figure 1608.2]

Snow Load S5 psf

Wind Loads

Basic wind speed (3-second gust) ranges from 90 to 105 mph in the area of interest. [2006 IBC, Figure 1609] The largest value is more conservative than the 100 mph gust provided in the project description.

Building Geometry

This structure is assumed to comply with the requirements for the Method 1 Simplified Procedure of ASCE 7-05 §6.4.

  • hmean=16 ft; 0.4 hmean = 6.4 ft; Least horiz. dim. = b=24.2 ft; 0.1b=32.4 ft
  • End zone: a = min(0.4 hmean, 0.1b) = a=2.4 ft
  • End zone length = 2a=4.8 ft

Wind Pressures

Building Height and Exposure, λ
Mean Building HeightExposure
hmeanBCD
15 1.00 1.21 1.47
(interpolated) 16 1.00 1.23 1.49
20 1.00 1.29 1.55

[Figure 6-2, ASCE 7-05]

The roof angle depends to a small degree on the dimensions of the roof members and is taken here conservatively as 15°.

ABCDEFGHEOHGOH
Basic ps30* 21.9 -7.3 14.7 -4.2 -21.1 -13.7 -14.7 -10.5 -29.4 -23.0
Adjusted W (ps)† 32.5 -10.8 21.8 -6.2 -31.4 -20.4 -21.8 -15.6 -43.7 -34.2
  • * from Figure 6-2,ASCE 7-05, h≤60', 105 mph design wind speed, 15° Roof Angle, Load Case 1
  • †I=1.0 ; Kzt=1.0 ; λ=1.47+ (16-15)*{{1.55-1.47}/{20-15}}=1.47+0.016=1.486 ; p_s=lambda K_{zt} I p_{s30}

Seismic Loads

The buildings are assumed to be placed in locations with conditions consistent with seismic design category A. Specifically, these will not be erected on sites with very poor soils and the other seismic criteria in this part of Texas are consistent with design category A.

There is only one level to consider at which the dead load of the roof weight combines with half the wall weight. Assume the walls will be no heavier than fully-grouted CMU, 120 pcf

  • P_r=p_r A_r =17.1*1490=25479 lb
  • P_w=120 t_w{{A_w}/2}=120*{7.625/12}*16*(2*39.2+2*24.2)=154696 lb
  • D_r=P_r+P_w=25479+154696=180175 lb
  • F_{r}=0.01 omega_{r,long}=0.01*180175=1800 lb
Design Lateral Force at Roof Level 1800 lb

However, lateral wind loads are much greater and control this design.

  • P_{W,lat} > 16*24.2*21.8=8441 » 1800
  • P_{W,long} > 16*39.2*6.2=3889 » 1800

Other Loads

No other loads are considered for this simple, small, one-story building. Control joints are assumed to be located in the CMU structure as required by applicable codes.

Load Combinations

The worst-case LRFD loadings are indicated in bold in the table below. Gravity loads are vertical downward loads while environmental loads may have both horizontal and vertical components and are expressed in various units.

Load CombinationCalculationGravity Load (psf)Lateral LoadλLoad/λ
1.4D 1.4×17.1= 24 0 0.6 40
1.2D + 1.6L + 0.5(Lr or S) 1.2*17.1+0+0.5×20= 31 0 1.25 24.8
1.2D + 1.6(Lr or S) + (L or 0.8W) 21+32+0.8W= 53 0.8W 0.8 66+W
1.2D + 1.6W + L + 0.5(Lr or S) 21+1.6W+0+10= 31 1.6W 1.0 31+1.6W
1.2D + 1.0E +L +0.2S 21+E+0+1= 22 E 1.0 22+E
0.9D + 1.6W 0.9×17.1+1.6W= 15 1.6W 1.0 15+1.6W
0.9D + E 0.9×17.1+E= 15 E 1.0 15+E

[ASCE 7 §2.3.2]

  • (Lr or S)=max(20,5)=20
  • (L or 0.8W)=max(0,0.8W)=0.8W
  • Lateral wind loads are much greater than seismic loads and control wall shear and bending design.
    • P_{W,lat} > 16*24.2*21.8=8441 » 1800
    • P_{W,long} > 16*39.2*6.2=3889 » 1800

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