Homework 1 (Due Monday, September 10)

David Wagner 2007/09/03 11:57

Solve the following problems from your textbook using the changes indicated. Solutions to some of these problems are available under practice problems in WebCT.

Problem 2.3.

Change the roof cover from 5-ply with gravel to 3-ply with gravel. Change the truss weight from 9 lb/ft to 12 lb/ft. Change the plywood in the roof from ½” to ¾”.

a. Roof dead load D in psf

Roofing (3-ply with gravel) 5.6 psf
Reroofing 2.5
¾” Plywood (¾*3) 2.25
Trusses (12 lb/ft / 2) 6
Suspended Ceiling (acoustical tile) 1.0
Total 17.35
Roof Dead Load D 17.5 psf

b. Second-floor dead load D in psf

Movable partitions
1½” Concrete @ 150 pcf* 18.75 psf
5/8” T&G Plywood (5/8 *3) 1.875
2×10 @ 16” 5.7
Air Duct 0.5
Suspended Ceiling (acoustical tile) 1.0
Total 27.825
Second-floor dead load D 28 psf

*It looks like the 150 psf figure in the textbook is incorrect

c. Basic (i.e. consider roof slope but not tributary area) unit roof live load Lr in psf

Roof is flat so no reduction. R_1=1; R_2=1; L_r=L_0*R_1*R_2=20*1*1=20; 12 ≤ 20 ≤ 20✔

Basic Unit Roof Live Load Lr 20 psf

Problem 2.5.

Change the ridge beam spans from 20 ft to 25 ft.

a. Tributary area to the ridge beam

Assume gables do not support significant roof weight.

A_T =13*25=325 sf

b. Roof live load Lr in lb/ft

L_r = L_0 R_1 R_2 = 20*(1.2-0.001*325)*1=17.5 psf

17.5 * 26=455 lb/ft

455 lb/ft of entire house length
227.5 lb/ft of ridge beam supporting tributary area

Problem 2.7.

For the snow load assume the structure located in Childress, TX. Maintain the same exposure.

Figure 2.B, standard residential occupancy, heated building, a ground snow load of 70 psf, and Exposure C terrain with a fully exposed roof. Find the design snow load S in psf on a horizontal plane.

  • The ground snow load looks to be about pg=10 psf.
  • Category II → I=1.0
  • Exposure factor Ce=0.9
  • Thermal factor Ct=1.0

S=p_f=0.7 C_e C_t I P_g = 0.7*0.9*1.0*1.0*10=6.3

6.3 psf

Problem 2.10.

Change the snow load from 25 psf to 30 psf.

The roof structure in Fig. 2.D and a 25 30-psf design snow load specified by the building official.

a. Uniformly distributed snow load S in lb/ft for

a1. 2×4 subpurlin w=A_T S =2*8*30=480

480 lb/ft

a2. 4×14 purlin w=A_T S =8*20*30=4800

4800 lb/ft

a3. 6-3/4 x 33 glulam beam w=A_T S =20*50*30=30000

30000 lb/ft

b. Tributary snow load S to column C1 in k w=A_T S =20*50*30=30000

30000 lb/ft

Problem 2.13.

Change the beam spans from 26 ft to 28 ft and the tributary width from 16 ft to 18 ft.

An interior beam supports the floor of a classroom in a school building. The beam spans 26 28 ft. and the tributary width is 16 18 ft. Dead load = 20psf.

a. Basic floor live load L0 in psf

Classroom [Table 1607.1]40 psf

b. Reduced floor live load L in psf

A_T = 28*18=504 sf; KLL=2

K_{LL}A_T =2*504=1008 ≥ 400 → L=L_0(0.25+{15/{sqrt{K_{LL} A_T}}}) = 40(0.25+{15/{sqrt{1008}}}) = 0.722L_0=0.722*40=28.89 approx29 psf

L > 0.5L0

29 psf

c. Uniformly distributed total load to the beam in lb/ft

w=(D+L)l=(20+29)*28=1372

1372 lb/ft

d. Compare the loading in part c with the alternate concentrated load required by the Code. Which loading is more critical for bending, shear and deflection?

w=1372 lb/ft is numerically larger than the P=1000 lb concentrated load specified in the code.

LimitMore Critical Loading
Bendingw
ShearP over span, w at ends
Deflectionw

Problem 2.20.

Part a ONLY. No changes. Hint: use Example 2.8.

The enclosed building in Fig. 2.E is a two-story essential facility located near Denver, Colorado. Wind Exposure C applies.

a. The design wind pressures in both principal directions of the building for main wind force-resisting systems.

Roof angle: atan(3/12)=14 approx15º Building height: 22 + {50/2}*{3/12}=22+6.25=28.25'

Ps30=90; Category IV → I=1.15; Kzt=1.0 (Assume at least one criterion is not met);

λ=1.35 + (1.40-1.35)*{28.25-25} / {30-25}=1.35+0.05*0.65=1.3825;

p_s = lambda K_{zt} I p_{s30}=1.3825*1.0*1.15*p_{s30}=1.589875 p_{s30} approx1.6 ps30

Roof AngleLoad CaseABCDEFGHEOHGOH
ps30 15° 1 16.1 -5.4 10.7 -3.0 -15.4 -10.1 -10.7 -7.7 -21.6 -16.9
ps 15° 1 25.6 -8.6 17.0 -4.8 -24.5 -16.1 -17.0 -12.2 -34.3 -26.9

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