Problem 7.5

 

Given

 

Member size 2x6 lower chord
Load D = 20 psf and S = 55 psf on upper chord
D = 5 psf on lower chord (20 lb/ft)
Stress grade and species No. 1 DF-L
Fasteners ignore
Adjustment factors CM = 1
Ct = 1
Ci = 1

Assume pin-connected truss at 4 ft OC.

 

 

Size (NDS Supplement table 1B)

 

Ag = 8.250 in.2
An = Ag - 1.5 in. x (XX in. + 1/16 in.) = XX in.2  (NDS section 11.1.2.2 and appendix L table L1)
Sxx = 7.563 in.3
Ixx = 20.80 in.4

 

 

Load Combinations

 

Load Symbol Given Value (psf)
(acting downward)
dead load D 20, 5
weight of ice Di 0
earthquake load E 0
load due to fluids F 0
flood loads Fa 0
load due to sub-surface pressure H 0
live load L 0
roof live load Lr 0
rain load R 0
snow load S 55
self-straining force T 0
wind load W 0
wind-on-ice Wi 0

 

ASCE 7 section 2.4

ASCE 7 IBC ASD Load Combination Possible Values (psf)
1 16-8 D + F 20
2 16-9 D + H + F + L + T 20
3 16-10 D + H + F + (Lr or S or R) 75
4 16-11 D + H + F + 0.75(L + T) + 0.75(Lr or S or R) 61.25
5 16-12 D + H + F + (W or 0.7E) 20
6 16-13 D + H + F + 0.75(W or 0.7E) + 0.75L + 0.75(Lr or S or R) 61.25
7 16-14 0.6D + W + H --A
8 16-15 0.6D + 0.7E + H --A

A Combinations 7 and 8 are not applicable because S is acting in the same direction (downward) as D.  See highlighted paragraph in ASCE 7 section C2.4.

 

(D)max = 20 psf
(D+S)max = 75 psf  (D+0.75S) involves the same load types and is smaller.

 

 

Adjusted Design Values

 

NDS Supplement table 4A

Cr = 1 (more than 24 in. OC)
CM = 1 (given)
CF = 1.3 for Fb, 1.3 for Ft, 1.1 for Fc
Cfu = 1

NDS Supplement section 2.3

CD = 0.9 (D) or 1.15 (D+S) depending on load combination
Ct = 1 (given)

 NDS Supplement section 3.3

CL = 1 (see below)

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)

 NDS section 3.3.3.2 says, "When rectangular sawn lumber bending members are laterally supported in accordance with 4.4.1, CL = 1.0."

d/b = 5.5 in./1.5 in. = 3.67

NDS section 4.4.1.2 says, "2 < d/b < 4; the ends shall be held in position, as by full depth solid blocking, bridging, hangers, nailing, or bolting to other framing members, or other acceptable means."

Assume that this bracing is provided in lower chord.

Property Reference Design
Values (psi)
(Table 4A)		 Adjustment Factors (Table 4.3.1) Adjusted Design
Values (psi)
CD CM Ct CL CF Cfu Cr CP Ci CT Cb
bending stress Fb 1,000 0.9 or 1.15 1 1 1 1.3 1 1   1     1,170 or 1,495
tension stress parallel to grain Ft 675 0.9 or 1.15 1 1   1.3       1     790 or 1,009
shear stress parallel to grain Fv 180 0.9 or 1.15 1 1           1     --
compression stress perpendicular to grain Fc⊥ 625   1 1           1   1 --
compression stress parallel to grain Fc 1,500 0.9 or 1.15 1 1   1.1     1 1     --
modulus of elasticity (or MOE) E 1,700,000   1 1           1     --
modulus of elasticity for stability calculations Emin 620,000   1 1           1 1   --

 

 

Actual Stress for (D) Load Combination (ASD)

 

Check tension stress...

Load at pins A and C = 20 psf x 2.5 ft x 4 ft =  200 lb  (these pass directly into ground connections and do not influence truss)
Load at other pins in upper chord = 20 psf x 5 ft x 4 ft = 400 lb
Load at other pin in lower chord = 5 psf x 10 ft x 4 ft = 200 lb

Height of truss peak = 10 ft x 5/12 = 4.167 ft  (needed for drawing truss)
Height of intermediate nodes = 5 ft x 5/12 = 2.083 ft  (estimated from given diagram)


truss_1.rtd

Load in bottom chord = 1.68 kip (T)  (Autodesk Robot, negative values represent tension)

ft = P/An = 1,680 lb / 8.250 in.2 = 204 psi ≤ 790 psi  ✓

It is conservative to consider bending alone in the bottom chord members...

wD = 5 psf x 4 ft = 20 lb/ft
Vmax = 20 lb/ft x 10 ft / 2 = 100 lb
Mmax = 0.5 x 5 ft x 100 lb = 250 lb-ft x 12 in./ft = 3,000 lb-in.

fb = M/S = 3,000 lb-in. / 7.563 in.3 = 397 psi ≤ 1,170 psi  ✓

Check formulas in NDS section 3.9.1 for combined axial tension and bending...

ft/F't + fb/F*b = 204/790 + 397/1,170 = 0.598 ≤ 1.0  ✓
(fb-ft)/F**b = (397-204)/1,170 = 0.165 ≤ 1.0  ✓

 

 

Actual Stress for (D+S) Load Combination (ASD)

 

Check tension stress...

Load at pins A and C = 75 psf  x 2.5 ft x 4 ft + 5 psf x 5 ft x 4 ft =  850 lb  (these pass directly into ground connections and do not influence truss)
Load at other pins in upper chord = 75 psf x 5 ft x 4 ft = 1,500 lb
Load at other pin in lower chord = 5 psf x 10 ft x 4 ft = 200 lb


truss_2.rtd

Load in bottom chord = 5.64 kip (T)  (Autodesk Robot, negative values represent tension)

 ft = P/An = 5,640 lb / 8.250 in.2 = 684 psi ≤ 1009 psi  ✓

It is conservative to consider bending alone in the bottom chord members...

wD = 5 psf x 4 ft = 20 lb/ft
Vmax = 20 lb/ft x 10 ft / 2 = 100 lb
Mmax = 0.5 x 5 ft x 100 lb = 250 lb-ft x 12 in./ft = 3,000 lb-in.

fb = M/S = 3,000 lb-in. / 7.563 in.3 = 397 psi  ≤ 1,495 psi ✓

Check formulas in NDS section 3.9.1 for combined axial tension and bending...

ft/F't + fb/F*b = 684/1009 + 397/1,495 = 0.943 ≤ 1.0  ✓
(fb-ft)/F**b = (397-684)/1,495 = -0.192 ≤ 1.0  ✓