Question

16 The truss in Fig. 7.B supports a roof dead load of 16 psf. Trusses are spaced 24-in. о.с., and the roof live load is to be in accordance with the IBC. Lumber is No. 2 DF-L. Fasteners do not reduce the area of the members. Truss joints are assumed to be pin-connected. CM 1.0, C, 1.0, and C,-1.0 Find: aThe required member size for the tension (bottom) chord using ASD. b. The required member size for the tension (bottom) chord using LRFD. Figure 7.B

Answer 1

From the question D 16 psf L,-1 x 1 x 20 psf-20 psf (Ar-42 ft. x 2 ft.-84 sqft < 200 sqft, 7:21 = 4:12; ASCE 7 table 4-1 and section 4.9.1) Oa Stress grade and No. 2 DF-L species Fasteners Do not reduce the area of members so ignore Adjustment factors (M=1 Load Combinations Given Value (psf)(acting downward) Load Dead load D Weight of ice Di Earthquake load E 0 Load due to fluids F 0 Flood loads Fa 0 Load due to sub-surface pressure Live load L Roof live load L Rain load R Snow load S Self-straining force T Wind load W 0 0 20 0 0 Wind-on-ice Wi 0

Basic Combinations Possible Values (psf) 16+0-16 16+0-16 16+20-36 16+0.75 x 20-31 16+0-16 ASCE 7ASD Load Combination D+F D+H+F+(Lr or S or R) D+H+F +0.75(L T) +0.75(L or S or R) D+H+F(W or 0.7E) D+H+F+ 0.75(W or 0.7E) +0.75L +0.75(L or S or R) 16+0.75 x 20-31 3 6 Combinations 7 and 8 from ASCE 7 are not applicable because S is acting in the same direction (downward) as D (Dr36 psf Trial Size Based on (D+Lr) Load Combination (ASD) Load at pins A and C- 36 psf x 5.25 ft. x 2 ft. -396 lb (these pass directly into ground connections and do not influence truss) Load at other pins in upper chord - 36 psfx 10.5 ft. x 2 ft. - 756 lb 76 FZ-0.76 FZ--0.76 3.40 3.40 40 FZ-1.13 FZ-1.13 Load in bottom chord 3.4 kip (Tension) 4.,-P/F',- 3400 / (575psz x 1.25) = 4.73 in' (NDS Supplement lable 4A, Cu-1.25) 1T1

A 3.750 in.2 (NDS Supplement table 1B) A25.250 in.' Adjusted Design Values NDS Supplement table 4A Cr1.15 if 2"-4" thick members CM= I (given) C 1.5 for Fh, 1.5 for Ft, 1.15 for Fe for both 2x3 and 2x4 Ca-I (not a beam) NDS Supplement section 2.3 Cp 0.9 (D) or 1.25 (D+Lr) depending on load combination 1 (given) NDS Supplement section 3.3 Cz= 1 (no compression) NDS Supplement section 3.7 Cp 1 (not a column) NDS Supplement section 3.10 Cb-1 (not enough info given) NDS Supplement section 4.3 Ci-1 (given) NDS Supplement section 4.4 CT-1 (not compression chord)

Reference Design Values (psi) Adjusted Design Adjustment Factors (Table 4.3.1) Property Values (psi) (Table 4A)C 0.9 or 1.25I 0.9 or 1.25 1 0.9 or 1.25 1 bending stress tension stress parallel to grain shear stress parallel to grain compression stress perpendicular to grain 900 11.15 Fr 776 or 1078 Fv 180 625 compression stress parallel tolc grain 1,350 0.9 o 1.25I 1.15 modulus of elasticity (or MOE) 16,00,000 modulus of elasticity for stability calculations Lmin5,80,000

Actual Stress for (D) Toad Combination (ASD) Load at pins A and (- 16 psf x5.25 fi 2 ft-168 lb (these pass directly into ground connections and do not influence truss) Load at other pins in upper chord - 16psf x10.5fix2fi - 336 Ib FZ--0.34 -0.34 FZ--0.34 1.51 1.51 1.51 1.51 FZ-0.50 FZ-0.50 Load in bottom čhord = 1.51 kip (Tension) 1,510 lb-= 403 psi PiAn3.750 in So OK 776 psi 2x.3 1,510 lb 5.250 in 5-288 psi 776 psi So OK Actual Stress for (D+Li) Load Combination (ASD)) Load at pins A and C-36 psfx5.25 ftx 2 fi - 396 lb (these pass directly into ground connections and do not influence truss) Load al other pins in upper chord 36 pof × 10.5ft×2ft-756 lb

FZ -0.76 FZ-0.76 FZ--0.76 3.40 3.40 40 FZ-1.13 FZ-1.13 Load in botlom chord3.4 kip (Tension) 23 PIA3,400 lb "3.750 in. 907 psi 1078 psi So OK 12x3- 3.750 in2 ft 2x4-PI A= 3,400 lb 5.250 in 648 psi 1078 psi So OK " A 2x3 or larger would work