Problem 3.1

 

 

Dead Load

 

D = 13 psf  (given)

 

Roof Live Load

 

L₀ = 20 psf  (IBC table 1607.1)

A_T = 20 x 8 = 160 sqft for P1  (IBC section 1607.11.2.1)
A_T = 20 x 48 = 960 sqft for G1
A_T = 20 x 32 = 640 sqft for G2
A_T = 20 x 16 = 320 sqft for G3

R₁ = 1 for P1
R₁ = 0.6 for G1
R₁ = 0.6 for G2
R₁ = 1.2-0.001A_T = 0.88 for G3

R₂ = 1 for P1, G1, G2 and G3  (flat roof)

L_r = L₀R₁R₂ 
L_r = 20 psf for P1
L_r = 12 psf for G1
L_r = 12 psf for G2
L_r = 17.6 psf for G3
(Note that these are higher for smaller areas.)

 

Total Load

 

D + L_r = 33 psf for P1
D + L_r = 25 psf for G1
D + L_r = 25 psf for G2
D + L_r = 30.6 psf for G3

w_D+Lr = 33 x 8 = 264 lb/ft for P1
w_D+Lr = 25 x 20 = 500 lb/ft for G1
w_D+Lr = 25 x 20 = 500 lb/ft for G2
w_D+Lr = 30.6 x 20 = 612 lb/ft for G3

Assume concentrated loads from purlins into girders

Force on P1 = 264 x 20 = 5,280 lb
(It is interesting to see how much higher this is, but it's probably a bit too high since D includes the weight of the girders, which the purlins wouldn't carry.)
Force on G1 for each P1 = 500 x 8 = 4,000 lb
Force on G2 for each P1 = 500 x 8 = 4,000 lb
Force on G3 for each P1 = 612 x 8 = 4,896

Assume distributed loads acting directly on girders

Force on G1 for its entire A_T = 500 x 48 = 24,000 lb
Force on G2 for its entire A_T = 500 x 32 = 16,000 lb
Force on G3 for its entire A_T = 612 x 16 = 9,792 lb
(The ground reactions in the following images add up to these values.  This was just a check.)

 

Comparison for G1

 

g1_comparison.rtd

 

Comparison for G2

 

g2_comparison.rtd

 

Comparison for G3

 

g3_comparison.rtd 

 

Suggestion from section 3.2

 

For live loads, use tributary area of member being designed instead of loads from smaller members.