Problem 9.7

 

Given

 

Application	single-story commercial building
Panel	15/32-in. thick 32/16 span-rated STRUCTURAL I sheathing
Edge Support	unblocked
Nails	8d common
Critical lateral forces	wu = wT = 320 lb/ft  (strength level seismic, transverse direction) wu = wL = 570 lb/ft  (strength level seismic, longitudinal direction)

Figure 9.A

 

 

a. Adjusted chord forces: maximum and at each end of wall openings

 

Transverse Loading

Middle of 80-ft wall

Maximum moment:  M_u = w_TL²/8 = 320 lb/ft (80 ft)² / 8 = 256,000 lb-ft  (see moment diagram above)

Maximum LRFD tension & compression:  T_u = C_u = M_u/b = 256,000 lb-ft / 35 ft = 7,314 lb

Maximum ASD tension & compression:  T = C = 0.7T_u =  5,120 lb

 

West end of header in 80-ft wall

V_max = R = w_T (80 ft) / 2 = (320 lb/ft)(80 ft) / 2 = 12,800 lb

By similar triangles on V diagram, 

V_max / 40 ft = V_west / 25 ft

V_west = 8,000 lb

M_west = M_u = area under first portion of the V diagram = 15 ft x V_west + 0.5 x 15 ft x (V_max - V_west) = 156,000 lb-ft

T_u = C_u = M_u/b = 156,000 lb-ft / 35 ft = 4,457 lb

T = C = 0.7T_u =  3,120 lb

 

East end of header in 80-ft wall

V_max = R = w_T (80 ft) / 2 = (320 lb/ft)(80 ft) / 2 = 12,800 lb

By similar triangles on V diagram, 

V_max / 40 ft = V_east / 20 ft

V_east = 6,400 lb

M_east = M_u = area under last portion of the V diagram = 20 ft x V_east + 0.5 x 20 ft x (V_max - V_east) = 192,000 lb-ft

T_u = C_u = M_u/b = 192,000 lb-ft / 35 ft = 5,486 lb

T = C = 0.7T_u =  3,840 lb

 

 

Longitudinal Loading

 

Middle of 35-ft wall

Maximum moment:  M_u = w_Lb²/8 = 570 lb/ft (35 ft)² / 8 = 87,280 lb-ft  (see moment diagram above)

Maximum LRFD tension & compression:  T_u = C_u = M_u/L = 87,280 lb-ft / 80 ft = 1,091 lb

Maximum ASD tension & compression:  T = C = 0.7T_u =  763.7 lb

 

North end of header in 35-ft wall

V_max = R = w_L (35 ft) / 2 = (570 lb/ft)(35 ft) / 2 = 9,975 lb

By similar triangles on V diagram, 

V_max / 17.5 ft = V_north / 2.5 ft

V_north = 1,425 lb

M_north = M_u = area under last portion of the V diagram = 15 ft x V_north + 0.5 x 15 ft x (V_max - V_north) = 85,500 lb-ft

T_u = C_u = M_u/b = 85,500 lb-ft / 80 ft = 1,069 lb

T = C = 0.7T_u =  748.1 lb

 

South end of header in 35-ft wall

M_south = M_u = 0

T_u = C_u = M_u/b = 0

T = C = 0.7T_u =  0

 

 

b. Plot strut forces for walls with openings

 

Transverse Loading

V_max = R = w_T (80 ft) / 2 = (320 lb/ft)(80 ft) / 2 = 12,800 lb

v_roof = R/b = 12,800 lb / 35 ft = 365.7 lb/ft
v_wall = R/b = 12,800 lb / 15 ft = 853.3 lb/ft

 

North end of header in 35-ft wall

T_u = C_u = (15 ft) |v_wall - v_roof| = (15 ft) | 853.3 lb/ft - 365.7 lb/ft | = 7,314 lb

T = C = 0.7T_u = 5,120 lb

 

Middle of 35-ft wall

T_u = C_u = (15 ft) |v_wall - v_roof| - 2.5 ft (v_roof) = (15 ft) | 853.3 lb/ft - 365.7 lb/ft | - 2.5 ft (365.7 lb/ft) = 6,400 lb

T = C = 0.7T_u = 4,480 lb

 

South end of header in 35-ft wall

T_u = C_u = 0

T = C = 0.7T_u =  0

 

 

Longitudinal Loading

V_max = R = w_L (35 ft) / 2 = (570 lb/ft)(35 ft) / 2 = 9,975 lb

v_roof = V/b = 9,975 lb / 80 ft = 124.7 lb/ft
v_wall = V/b = 9,975 lb / 35 ft = 285.0 lb/ft

 

West end of header in 80-ft wall

T_u = C_u = (15 ft) |v_roof - v_wall| = (15 ft) | 124.7 lb/ft - 285.0 lb/ft | = 2,405 lb

T = C = 0.7T_u = 1,684 lb

 

Middle of 80-ft wall

T_u = C_u = | (40 ft) (v_roof) - 15 ft (v_wall) | = | (40 ft) (124.7 lb/ft) - 15 ft (285.0) | = 713 lb

T = C = 0.7T_u = 499.1 lb

 

East end of header in 80-ft wall

T_u = C_u = (20 ft) |v_roof - v_wall| = (20 ft) | 285.0 lb/ft - 124.7 lb/ft | = 3,206 lb

T = C = 0.7T_u = 2,244 lb

 

 

b. Compare chord and strut forces

 

LRFD values

Location		Transverse Loading		Longitudinal Loading
		Chord force (lb)	Strut force (lb)	Chord force (lb)	Strut force (lb)
80-ft wall	west end of header	4,457			2,405
	middle of wall	7,314			713
	east end of header	5,486			3,206
35-ft wall	north end of header		7,314	1,069
	middle of wall		6,400	1,091
	south end of header		0	0

∴ Chord force > strut force at a particular point for transverse loading; Chord force < strut force at a particular point for longitudinal loading

Maximum load = 7,314 lb

 

ASD values

Location		Transverse Loading		Longitudinal Loading
		Chord force (lb)	Strut force (lb)	Chord force (lb)	Strut force (lb)
80-ft wall	west end of header	3,120			1,684
	middle of wall	5,120			499
	east end of header	3,840			2,244
35-ft wall	north end of header		5,120	748
	middle of wall		4,480	764
	south end of header		0	0

Maximum load = 5,120 lb