PROJECT :

CLIENT :
JOB NO. : DATE :
Formulas of Moment Resisting Frame at Bottom Fixed Condition

INPUT DATA & DESIGN SUMMARY

BEAM SECTION W16X26 W Shape Ib = 301
ORIENTATION (x-x, y-y) x-x , (strong axis bending) ( 12529

COLUMN SECTION W10X30 W Shape Ic = 170

ORIENTATION (x-x, y-y) x-x , (strong axis bending) ( 7076

BEAM LENGTH BETWEEN COL. CENTERS L= 30 ft, (9.1 m)

STORY HEIGHT h= 14 ft, (4.3 m)

GRAVITY LOAD w= 1.8 klf, (26 kN / m)

HA = HD = 10.2 kips MB = M C = 95.5 ft-kips
VA = V D = 27.0 kips Mmax = 107.0 ft-kips
MA = M D = 47.8 ft-kips

LATERAL LOAD P= 15 kips, (66.7 kN)

HA = HD = 7.5 kips MB = M C = 43.7 ft-kips
VA = V D = 2.9 kips DH = 0.90 in
MA = M D = 61.3 ft-kips KH = 16.6 kips / in
(KH is frame stiffness.)

GRAVITY ANALYSIS

h wL
n  Ib  0.826 V A V D   27.0 kips
Ic L 2

wL 2 wL 2
HAHD  10.2 kips MAMD 
4h  2  n  12  2  n 
 wL 2 wL 2
HAHD  MAMD 
4h  2  n  12  2  n 

w L 2  2  3n  wL 2
M max   107.0 ft-kips MB  MC  
24  2  n  6  2  n

LATERAL ANALYSIS

 3n   3n  1 
a  h  5.83 ft b  h  8.17 ft
 6n  1   6n  1 

3nPh Ph  1  3n 
V A V D   2.9 kips MAMD 
L  1  6n  2  1  6n 

3nPh
E 29000 ksi MB  MC  
2  1  6n 
 3  a L 
P  b  a2   
 Ic  Ic 2I b  P
DH   0.90 in KH  
6E DH
 PAGE :
DESIGN BY :
REVIEW BY :

in4
cm4)

in4
cm4)

47.8 ft-kips
95.5 ft-kips

P 7.5 kips
HA HD 
2

61.3 ft-kips

43.7 ft-kips

16.6 kips / in
 PROJECT :
CLIENT :
JOB NO. : DATE :
Formulas of Moment Resisting Frame at Bottom Pinned Condition

INPUT DATA & DESIGN SUMMARY

BEAM SECTION W16X26 W Shape Ib = 301
ORIENTATION (x-x, y-y) x-x , (strong axis bending) ( 12529

COLUMN SECTION W10X33 W Shape Ic = 171

ORIENTATION (x-x, y-y) x-x , (strong axis bending) ( 7118

BEAM LENGTH BETWEEN COL. CENTERS L= 20 ft, (6.1 m)

STORY HEIGHT h= 14 ft, (4.3 m)

GRAVITY LOAD w= 1.8 klf, (26 kN / m)

HA = HD = 2.4 kips MB = M C = 32.9 ft-kips
VA = V D = 18.0 kips Mmax = 57.1 ft-kips

LATERAL LOAD P= 15 kips, (66.7 kN)

HA = HD = 7.5 kips MB = M C = 105.0 ft-kips
VA = V D = 10.5 kips DH = 3.36 in
KH = 4.5 kips / in
(KH is frame stiffness.)

GRAVITY ANALYSIS

h wL
n  Ib  1.232 V A V D   18.0 kips
Ic L 2

wL 2 wL 2
HA HD  MB MC  
4h  3  2 n  4  3  2n 
 wL 2 wL 2
HA HD  2.4 kips MB MC  
4h  3  2 n  4  3  2n 

w L 2  2n  1
M max   57.1 ft-kips
8  2n  3 

LATERAL ANALYSIS
P
HA HD   7.5 kips E 29000
2

Ph Ph
V A V D   10.5 kips MBMC  
L 2

P h 3  1  2n  P
DH   3.36 in KH  
12nE I c DH
 PAGE :
DESIGN BY :
REVIEW BY :

in4
cm4)

in4
cm4)
 32.9 ft-kips

ksi

105.0 ft-kips

4.5 kips / in
 PROJECT :
CLIENT :
JOB NO. : DATE :
Formulas of Concentrically Braced Frame

INPUT DATA & DESIGN SUMMARY

BRACE SECTION HSS6X6X1/2 Tube EA = 282460

BEAM LENGTH BETWEEN COL. CENTERS L= 30 ft, (9.1 m)

STORY HEIGHT h= 14 ft, (4.3 m)

GRAVITY LOAD w= 1.8 klf, (26 kN / m)

HA = HD = 18.1 kips MBE = MEC = 28.5 ft-kips
VA = V D = 27.0 kips ME = 50.6 ft-kips
NAE = NDE = 24.7 kips NAB = NDC = 10.1 kips

LATERAL LOAD P= 15 kips, (66.7 kN)

HA = HD = 7.5 kips - NAE = NDE = 10.3 kips
VA = V D = 7.0 kips - NAB = NDC = 0.0 kips
DH = 0.01 in
KH = 1226.2 kips / in , (KH is frame stiffness.)

GRAVITY ANALYSIS (Neglected axial deformations.)

 h  wL
  tan 1   43.03 0 V A V D  
 0.5 L  2

5wL 9wL 2
HA HD  M BE  M EC  
16 tan  512
 5wL 9wL 2
HA HD  18.1 kips M BE  M EC  
16 tan  512

5wL wL 2
N AE  N DE   24.7 kips ME  
16sin  32

LATERAL ANALYSIS
P Ph
HA HD  7.5 kips V A V D  
2 L

P
 N AE  N DE   10.3 kips
2 cos 

PL P
DH   0.01 in KH  
4 EAcos 3 DH
 PAGE :
DESIGN BY :
REVIEW BY :

kips

27.0 kips
 28.5 ft-kips

50.6 ft-kips

7.0 kips

1226.2 kips / in
 PROJECT :
CLIENT :
JOB NO. : DATE :
Formulas of Eccentrically Braced Frame

INPUT DATA & DESIGN SUMMARY

BRACE SECTION HSS6X6X1/2 Tube EA = 282460

BEAM SECTION W16X26 W Shape EI = 8729000

ORIENTATION (x-x, y-y) x-x , (strong axis bending)

BEAM LENGTH BETWEEN COL. CENTERS L= 30 ft, (9.1 m)

STORY HEIGHT h= 14 ft, (4.3 m)
LINK LENGTH e= 4 ft, (1.2 m)

GRAVITY LOAD w= 1.8 klf, (26 kN / m)

HA = HD = 16.0 kips MBE = MFC = 25.8 ft-kips
VA = V D = 27.0 kips ME = M F = 24.5 ft-kips
NAE = NDF = 23.5 kips NAB = NDC = 9.8 kips

LATERAL LOAD P= 15 kips, (66.7 kN)

HA = HD = 7.5 kips - NAE = NDF = 11.0 kips
ME = M F = 14.0 ft-kips - NAB = NDC = -1.1 kips
QEF = VA = VD = 7.0 kips DH = 0.04 in
(QEF is link shear force.) KH = 384.5 kips / in
(KH is frame stiffness.)

GRAVITY ANALYSIS (Neglected axial deformations.)

 h 
  tan 1   47.12 0 MEMF 
 0.5 L  0.5e 

M E  w L  e
wL 2
V A V D   27.0 kips 
HA HD 
2 h 8h
 M E  w L  e
wL 2
V A V D   
HA HD 
2 h 8h
w L  e  M
2

N AE  N DF  HA  23.5 kips M BE  M FC  
cos  32

LATERAL ANALYSIS

P Ph
HA HD  7.5 kips Q EF  V A  V D  
2 L

P Peh
 N AE  N DF   11.0 kips MEMF  
2cos  2L

Ph P h 2e 2
DH    0.04 in
2 EAcos 2 sin  12 EIL
 PAGE :
DESIGN BY :
REVIEW BY :

kips

kips-in2

MF 24.5 ft-kips , (by moment distribution procedure.)

w  L2  e2
 HD  ME   16.0 kips
h 8h
 w  L2  e2
 HD  ME  
h 8h
w L e  M E
2

BE  M FC    25.8 ft-kips
32 2

Ph
D   7.0 kips
L

14.0 ft-kips

P
KH   384.5 kips / in
DH