Frame Calculation - Example: 1

Frame's Data

1,220.00 kg/m 1,220.00 kg/m 1,220.00 kg/m

5 6 7 8
5 6 7
1 2 3 4
2.70 m

1 2 3 4

5.85 m 7.50 m 5.85 m

Node's Properties Units

node x-co y-co support Distance : m Point Load : kg
m m Shear & Axial Force : kg Distributed Load : kg/m
#1 0.00 0.00 Hinge Bending Moment : kg-m Moment Load : kg-m
#2 5.85 0.00 Fixed-end Deflecion : mm Area, A : cm2
#3 13.35 0.00 Fixed-end Reaction : kg Elastic Modulus, E : kg/cm2
#4 19.20 0.00 Fixed-end Moment of Inertia, I : cm4
#5 0.00 2.70
#6 5.85 2.70
#7 13.35 2.70
#8 19.20 2.70

Member's Properties
member from node to node Area, A Modulus, E Inertia, I
cm2 kg/cm2 cm4
#1 #1 #5 1,050.00 2.53E+05 78,750.00
#2 #2 #6 1,750.00 2.53E+05 3.65E+05
#3 #3 #7 1,750.00 2.53E+05 3.65E+05
#4 #4 #8 1,050.00 2.53E+05 78,750.00
#5 #5 #6 13,200.00 2.53E+05 5.32E+05
#6 #6 #7 13,200.00 2.53E+05 5.32E+05
#7 #7 #8 13,200.00 2.53E+05 5.32E+05

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 1
Frame Calculation - Example: 1

Load's Properties
load at member load type value @ from node @ to node
m m
#1 #5 1,220.00 kg/m 0.00E+00 0.00E+00
#2 #6 1,220.00 kg/m 0.00E+00 0.00E+00
#3 #7 1,220.00 kg/m 0.00E+00 0.00E+00

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
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Frame Calculation - Example: 1

Global DOF

14 17 20 23

15 18 21 24
5 13 6 16 7 19 8 22
5 6 7
21 52 83 11 4
2.70 m

3 6 9 12
1 1 2 4 3 7 4 10

5.85 m 7.50 m 5.85 m

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 3
Frame Calculation - Example: 1

Member Stiffness Matrix: Member #1

14

15
5 13
node #1 = (0.00 , 0.00)
node #5 = (0.00 , 2.70)
1
x2 - x1 0.00 - 0.00
2 c = cos = = = 0.00
L 2.70
3
y2 - y1 2.70 - 0.00
s = sin = = = 1.00
1 1 L 2.70

[k] = [T]T [k'] [T]

Local Stiffness Matrix: [k']

AE/L 0 0 -AE/L 0 0
0 12EI/L3 6EI/L2 0 -12EI/L3 6EI/L2

[k'] = 0 6EI/L2 4EI/L 0 -6EI/L2 2EI/L

-AE/L 0 0 AE/L 0 0
0 -12EI/L3 -6EI/L2 0 12EI/L3 -6EI/L2
0 6EI/L2 2AE/L 0 -6EI/L2 4EI/L

where, A = 0.10 m2, E = 2.53E+07 kN/m2, I = 7.88E-04 m4, L = 2.70 m

AE/L = 0.10 x 2.53E+07 / 2.70 = 9.83E+05

3 3
12EI/L = 12 x 2.53E+07 x 7.88E-04 / 2.70 = 12,130.98
2 2
6EI/L = 6 x 2.53E+07 x 7.88E-04 / 2.70 = 16,376.82
4EI/L = 4 x 2.53E+07 x 7.88E-04 / 2.70 = 29,478.28
2EI/L = 2 x 2.53E+07 x 7.88E-04 / 2.70 = 14,739.14

9.83E+05 - - (9.83E+05) - -
- 12,130.98 16,376.82 - (12,130.98) 16,376.82

then, [k'] = - 16,376.82 29,478.28 - (16,376.82) 14,739.14

(9.83E+05) - - 9.83E+05 - -
- (12,130.98) (16,376.82) - 12,130.98 (16,376.82)
- 16,376.82 14,739.14 - (16,376.82) 29,478.28

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 4
Frame Calculation - Example: 1

Global Stiffness Matrix: [k]

cos sin 0 0 0 0 - 1.00 - - - -

-sin cos 0 0 0 0 (1.00) - - - - -

[T] = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos sin 0 - - - - 1.00 -
0 0 0 -sin cos 0 - - - (1.00) - -
0 0 0 0 0 1 - - - - - 1.00

cos -sin 0 0 0 0 - (1.00) - - - -

sin cos 0 0 0 0 1.00 - - - - -

[T]T = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos -sin 0 - - - - (1.00) -
0 0 0 sin cos 0 - - - 1.00 - -
0 0 0 0 0 1 - - - - - 1.00

12,130.98 - (16,376.82) (12,130.98) - (16,376.82)

- 9.83E+05 - - (9.83E+05) -

then, [k] = (16,376.82) - 29,478.28 16,376.82 - 14,739.14

(12,130.98) - 16,376.82 12,130.98 - 16,376.82
- (9.83E+05) - - 9.83E+05 -
(16,376.82) - 14,739.14 16,376.82 - 29,478.28

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 5
Frame Calculation - Example: 1

Member Stiffness Matrix: Member #2

17

18
6 16
node #2 = (5.85 , 0.00)
node #6 = (5.85 , 2.70)
2
x2 - x1 5.85 - 5.85
5 c = cos = = = 0.00
L 2.70
6
y2 - y1 2.70 - 0.00
s = sin = = = 1.00
2 4 L 2.70

[k] = [T]T [k'] [T]

Local Stiffness Matrix: [k']

AE/L 0 0 -AE/L 0 0
0 12EI/L3 6EI/L2 0 -12EI/L3 6EI/L2

[k'] = 0 6EI/L2 4EI/L 0 -6EI/L2 2EI/L

-AE/L 0 0 AE/L 0 0
0 -12EI/L3 -6EI/L2 0 12EI/L3 -6EI/L2
0 6EI/L2 2AE/L 0 -6EI/L2 4EI/L

where, A = 0.17 m2, E = 2.53E+07 kN/m2, I = 3.65E-03 m4, L = 2.70 m

AE/L = 0.17 x 2.53E+07 / 2.70 = 1.64E+06

3 3
12EI/L = 12 x 2.53E+07 x 3.65E-03 / 2.70 = 56,161.90
2 2
6EI/L = 6 x 2.53E+07 x 3.65E-03 / 2.70 = 75,818.56
4EI/L = 4 x 2.53E+07 x 3.65E-03 / 2.70 = 1.36E+05
2EI/L = 2 x 2.53E+07 x 3.65E-03 / 2.70 = 68,236.70

1.64E+06 - - (1.64E+06) - -
- 56,161.90 75,818.56 - (56,161.90) 75,818.56

then, [k'] = - 75,818.56 1.36E+05 - (75,818.56) 68,236.70

(1.64E+06) - - 1.64E+06 - -
- (56,161.90) (75,818.56) - 56,161.90 (75,818.56)
- 75,818.56 68,236.70 - (75,818.56) 1.36E+05

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 6
Frame Calculation - Example: 1

Global Stiffness Matrix: [k]

cos sin 0 0 0 0 - 1.00 - - - -

-sin cos 0 0 0 0 (1.00) - - - - -

[T] = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos sin 0 - - - - 1.00 -
0 0 0 -sin cos 0 - - - (1.00) - -
0 0 0 0 0 1 - - - - - 1.00

cos -sin 0 0 0 0 - (1.00) - - - -

sin cos 0 0 0 0 1.00 - - - - -

[T]T = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos -sin 0 - - - - (1.00) -
0 0 0 sin cos 0 - - - 1.00 - -
0 0 0 0 0 1 - - - - - 1.00

56,161.90 - (75,818.56) (56,161.90) - (75,818.56)

- 1.64E+06 - - (1.64E+06) -

then, [k] = (75,818.56) - 1.36E+05 75,818.56 - 68,236.70

(56,161.90) - 75,818.56 56,161.90 - 75,818.56
- (1.64E+06) - - 1.64E+06 -
(75,818.56) - 68,236.70 75,818.56 - 1.36E+05

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 7
Frame Calculation - Example: 1

Member Stiffness Matrix: Member #3

20

21
7 19
node #3 = (13.35 , 0.00)
node #7 = (13.35 , 2.70)
3
x2 - x1 13.35 - 13.35
8 c = cos = = = 0.00
L 2.70
9
y2 - y1 2.70 - 0.00
s = sin = = = 1.00
3 7 L 2.70

[k] = [T]T [k'] [T]

Local Stiffness Matrix: [k']

AE/L 0 0 -AE/L 0 0
0 12EI/L3 6EI/L2 0 -12EI/L3 6EI/L2

[k'] = 0 6EI/L2 4EI/L 0 -6EI/L2 2EI/L

-AE/L 0 0 AE/L 0 0
0 -12EI/L3 -6EI/L2 0 12EI/L3 -6EI/L2
0 6EI/L2 2AE/L 0 -6EI/L2 4EI/L

where, A = 0.17 m2, E = 2.53E+07 kN/m2, I = 3.65E-03 m4, L = 2.70 m

AE/L = 0.17 x 2.53E+07 / 2.70 = 1.64E+06

3 3
12EI/L = 12 x 2.53E+07 x 3.65E-03 / 2.70 = 56,161.90
2 2
6EI/L = 6 x 2.53E+07 x 3.65E-03 / 2.70 = 75,818.56
4EI/L = 4 x 2.53E+07 x 3.65E-03 / 2.70 = 1.36E+05
2EI/L = 2 x 2.53E+07 x 3.65E-03 / 2.70 = 68,236.70

1.64E+06 - - (1.64E+06) - -
- 56,161.90 75,818.56 - (56,161.90) 75,818.56

then, [k'] = - 75,818.56 1.36E+05 - (75,818.56) 68,236.70

(1.64E+06) - - 1.64E+06 - -
- (56,161.90) (75,818.56) - 56,161.90 (75,818.56)
- 75,818.56 68,236.70 - (75,818.56) 1.36E+05

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 8
Frame Calculation - Example: 1

Global Stiffness Matrix: [k]

cos sin 0 0 0 0 - 1.00 - - - -

-sin cos 0 0 0 0 (1.00) - - - - -

[T] = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos sin 0 - - - - 1.00 -
0 0 0 -sin cos 0 - - - (1.00) - -
0 0 0 0 0 1 - - - - - 1.00

cos -sin 0 0 0 0 - (1.00) - - - -

sin cos 0 0 0 0 1.00 - - - - -

[T]T = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos -sin 0 - - - - (1.00) -
0 0 0 sin cos 0 - - - 1.00 - -
0 0 0 0 0 1 - - - - - 1.00

56,161.90 - (75,818.56) (56,161.90) - (75,818.56)

- 1.64E+06 - - (1.64E+06) -

then, [k] = (75,818.56) - 1.36E+05 75,818.56 - 68,236.70

(56,161.90) - 75,818.56 56,161.90 - 75,818.56
- (1.64E+06) - - 1.64E+06 -
(75,818.56) - 68,236.70 75,818.56 - 1.36E+05

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 9
Frame Calculation - Example: 1

Member Stiffness Matrix: Member #4

23

24
8 22
node #4 = (19.20 , 0.00)
node #8 = (19.20 , 2.70)
4
x2 - x1 19.20 - 19.20
11 c = cos = = = 0.00
L 2.70
12
y2 - y1 2.70 - 0.00
s = sin = = = 1.00
4 10 L 2.70

[k] = [T]T [k'] [T]

Local Stiffness Matrix: [k']

AE/L 0 0 -AE/L 0 0
0 12EI/L3 6EI/L2 0 -12EI/L3 6EI/L2

[k'] = 0 6EI/L2 4EI/L 0 -6EI/L2 2EI/L

-AE/L 0 0 AE/L 0 0
0 -12EI/L3 -6EI/L2 0 12EI/L3 -6EI/L2
0 6EI/L2 2AE/L 0 -6EI/L2 4EI/L

where, A = 0.10 m2, E = 2.53E+07 kN/m2, I = 7.88E-04 m4, L = 2.70 m

AE/L = 0.10 x 2.53E+07 / 2.70 = 9.83E+05

3 3
12EI/L = 12 x 2.53E+07 x 7.88E-04 / 2.70 = 12,130.98
2 2
6EI/L = 6 x 2.53E+07 x 7.88E-04 / 2.70 = 16,376.82
4EI/L = 4 x 2.53E+07 x 7.88E-04 / 2.70 = 29,478.28
2EI/L = 2 x 2.53E+07 x 7.88E-04 / 2.70 = 14,739.14

9.83E+05 - - (9.83E+05) - -
- 12,130.98 16,376.82 - (12,130.98) 16,376.82

then, [k'] = - 16,376.82 29,478.28 - (16,376.82) 14,739.14

(9.83E+05) - - 9.83E+05 - -
- (12,130.98) (16,376.82) - 12,130.98 (16,376.82)
- 16,376.82 14,739.14 - (16,376.82) 29,478.28

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 10
Frame Calculation - Example: 1

Global Stiffness Matrix: [k]

cos sin 0 0 0 0 - 1.00 - - - -

-sin cos 0 0 0 0 (1.00) - - - - -

[T] = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos sin 0 - - - - 1.00 -
0 0 0 -sin cos 0 - - - (1.00) - -
0 0 0 0 0 1 - - - - - 1.00

cos -sin 0 0 0 0 - (1.00) - - - -

sin cos 0 0 0 0 1.00 - - - - -

[T]T = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos -sin 0 - - - - (1.00) -
0 0 0 sin cos 0 - - - 1.00 - -
0 0 0 0 0 1 - - - - - 1.00

12,130.98 - (16,376.82) (12,130.98) - (16,376.82)

- 9.83E+05 - - (9.83E+05) -

then, [k] = (16,376.82) - 29,478.28 16,376.82 - 14,739.14

(12,130.98) - 16,376.82 12,130.98 - 16,376.82
- (9.83E+05) - - 9.83E+05 -
(16,376.82) - 14,739.14 16,376.82 - 29,478.28

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 11
Frame Calculation - Example: 1

Member Stiffness Matrix: Member #5

14 17 node #5 = (0.00 , 2.70)

node #6 = (5.85 , 2.70)
15 18
5 13 6 16
x2 - x1 5.85 - 0.00
5 c = cos = = = 1.00
L 5.85
y2 - y1 2.70 - 2.70
s = sin = = = 0.00
L 5.85

[k] = [T]T [k'] [T]

Local Stiffness Matrix: [k']

AE/L 0 0 -AE/L 0 0
0 12EI/L3 6EI/L2 0 -12EI/L3 6EI/L2

[k'] = 0 6EI/L2 4EI/L 0 -6EI/L2 2EI/L

-AE/L 0 0 AE/L 0 0
0 -12EI/L3 -6EI/L2 0 12EI/L3 -6EI/L2
0 6EI/L2 2AE/L 0 -6EI/L2 4EI/L

where, A = 1.32 m2, E = 2.53E+07 kN/m2, I = 5.32E-03 m4, L = 5.85 m

AE/L = 1.32 x 2.53E+07 / 5.85 = 5.70E+06

3 3
12EI/L = 12 x 2.53E+07 x 5.32E-03 / 5.85 = 8,063.19
2 2
6EI/L = 6 x 2.53E+07 x 5.32E-03 / 5.85 = 23,584.84
4EI/L = 4 x 2.53E+07 x 5.32E-03 / 5.85 = 91,980.88
2EI/L = 2 x 2.53E+07 x 5.32E-03 / 5.85 = 45,990.44

5.70E+06 - - (5.70E+06) - -
- 8,063.19 23,584.84 - (8,063.19) 23,584.84

then, [k'] = - 23,584.84 91,980.88 - (23,584.84) 45,990.44

(5.70E+06) - - 5.70E+06 - -
- (8,063.19) (23,584.84) - 8,063.19 (23,584.84)
- 23,584.84 45,990.44 - (23,584.84) 91,980.88

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 12
Frame Calculation - Example: 1

Global Stiffness Matrix: [k]

cos sin 0 0 0 0 1.00 - - - - -

-sin cos 0 0 0 0 - 1.00 - - - -

[T] = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos sin 0 - - - 1.00 - -
0 0 0 -sin cos 0 - - - - 1.00 -
0 0 0 0 0 1 - - - - - 1.00

cos -sin 0 0 0 0 1.00 - - - - -

sin cos 0 0 0 0 - 1.00 - - - -

[T]T = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos -sin 0 - - - 1.00 - -
0 0 0 sin cos 0 - - - - 1.00 -
0 0 0 0 0 1 - - - - - 1.00

5.70E+06 - - (5.70E+06) - -
- 8,063.19 23,584.84 - (8,063.19) 23,584.84

then, [k] = - 23,584.84 91,980.88 - (23,584.84) 45,990.44

(5.70E+06) - - 5.70E+06 - -
- (8,063.19) (23,584.84) - 8,063.19 (23,584.84)
- 23,584.84 45,990.44 - (23,584.84) 91,980.88

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 13
Frame Calculation - Example: 1

Member Stiffness Matrix: Member #6

17 20 node #6 = (5.85 , 2.70)

node #7 = (13.35 , 2.70)
18 21
6 16 7 19
x2 - x1 13.35 - 5.85
6 c = cos = = = 1.00
L 7.50
y2 - y1 2.70 - 2.70
s = sin = = = 0.00
L 7.50

[k] = [T]T [k'] [T]

Local Stiffness Matrix: [k']

AE/L 0 0 -AE/L 0 0
0 12EI/L3 6EI/L2 0 -12EI/L3 6EI/L2

[k'] = 0 6EI/L2 4EI/L 0 -6EI/L2 2EI/L

-AE/L 0 0 AE/L 0 0
0 -12EI/L3 -6EI/L2 0 12EI/L3 -6EI/L2
0 6EI/L2 2AE/L 0 -6EI/L2 4EI/L

where, A = 1.32 m2, E = 2.53E+07 kN/m2, I = 5.32E-03 m4, L = 7.50 m

AE/L = 1.32 x 2.53E+07 / 7.50 = 4.45E+06

3 3
12EI/L = 12 x 2.53E+07 x 5.32E-03 / 7.50 = 3,826.40
2 2
6EI/L = 6 x 2.53E+07 x 5.32E-03 / 7.50 = 14,349.02
4EI/L = 4 x 2.53E+07 x 5.32E-03 / 7.50 = 71,745.09
2EI/L = 2 x 2.53E+07 x 5.32E-03 / 7.50 = 35,872.54

4.45E+06 - - (4.45E+06) - -
- 3,826.40 14,349.02 - (3,826.40) 14,349.02

then, [k'] = - 14,349.02 71,745.09 - (14,349.02) 35,872.54

(4.45E+06) - - 4.45E+06 - -
- (3,826.40) (14,349.02) - 3,826.40 (14,349.02)
- 14,349.02 35,872.54 - (14,349.02) 71,745.09

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 14
Frame Calculation - Example: 1

Global Stiffness Matrix: [k]

cos sin 0 0 0 0 1.00 - - - - -

-sin cos 0 0 0 0 - 1.00 - - - -

[T] = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos sin 0 - - - 1.00 - -
0 0 0 -sin cos 0 - - - - 1.00 -
0 0 0 0 0 1 - - - - - 1.00

cos -sin 0 0 0 0 1.00 - - - - -

sin cos 0 0 0 0 - 1.00 - - - -

[T]T = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos -sin 0 - - - 1.00 - -
0 0 0 sin cos 0 - - - - 1.00 -
0 0 0 0 0 1 - - - - - 1.00

4.45E+06 - - (4.45E+06) - -
- 3,826.40 14,349.02 - (3,826.40) 14,349.02

then, [k] = - 14,349.02 71,745.09 - (14,349.02) 35,872.54

(4.45E+06) - - 4.45E+06 - -
- (3,826.40) (14,349.02) - 3,826.40 (14,349.02)
- 14,349.02 35,872.54 - (14,349.02) 71,745.09

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 15
Frame Calculation - Example: 1

Member Stiffness Matrix: Member #7

20 23 node #7 = (13.35 , 2.70)

node #8 = (19.20 , 2.70)
21 24
7 19 8 22
x2 - x1 19.20 - 13.35
7 c = cos = = = 1.00
L 5.85
y2 - y1 2.70 - 2.70
s = sin = = = 0.00
L 5.85

[k] = [T]T [k'] [T]

Local Stiffness Matrix: [k']

AE/L 0 0 -AE/L 0 0
0 12EI/L3 6EI/L2 0 -12EI/L3 6EI/L2

[k'] = 0 6EI/L2 4EI/L 0 -6EI/L2 2EI/L

-AE/L 0 0 AE/L 0 0
0 -12EI/L3 -6EI/L2 0 12EI/L3 -6EI/L2
0 6EI/L2 2AE/L 0 -6EI/L2 4EI/L

where, A = 1.32 m2, E = 2.53E+07 kN/m2, I = 5.32E-03 m4, L = 5.85 m

AE/L = 1.32 x 2.53E+07 / 5.85 = 5.70E+06

3 3
12EI/L = 12 x 2.53E+07 x 5.32E-03 / 5.85 = 8,063.19
2 2
6EI/L = 6 x 2.53E+07 x 5.32E-03 / 5.85 = 23,584.84
4EI/L = 4 x 2.53E+07 x 5.32E-03 / 5.85 = 91,980.88
2EI/L = 2 x 2.53E+07 x 5.32E-03 / 5.85 = 45,990.44

5.70E+06 - - (5.70E+06) - -
- 8,063.19 23,584.84 - (8,063.19) 23,584.84

then, [k'] = - 23,584.84 91,980.88 - (23,584.84) 45,990.44

(5.70E+06) - - 5.70E+06 - -
- (8,063.19) (23,584.84) - 8,063.19 (23,584.84)
- 23,584.84 45,990.44 - (23,584.84) 91,980.88

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 16
Frame Calculation - Example: 1

Global Stiffness Matrix: [k]

cos sin 0 0 0 0 1.00 - - - - -

-sin cos 0 0 0 0 - 1.00 - - - -

[T] = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos sin 0 - - - 1.00 - -
0 0 0 -sin cos 0 - - - - 1.00 -
0 0 0 0 0 1 - - - - - 1.00

cos -sin 0 0 0 0 1.00 - - - - -

sin cos 0 0 0 0 - 1.00 - - - -

[T]T = 0 0 1 0 0 0 = - - 1.00 - - -
0 0 0 cos -sin 0 - - - 1.00 - -
0 0 0 sin cos 0 - - - - 1.00 -
0 0 0 0 0 1 - - - - - 1.00

5.70E+06 - - (5.70E+06) - -
- 8,063.19 23,584.84 - (8,063.19) 23,584.84

then, [k] = - 23,584.84 91,980.88 - (23,584.84) 45,990.44

(5.70E+06) - - 5.70E+06 - -
- (8,063.19) (23,584.84) - 8,063.19 (23,584.84)
- 23,584.84 45,990.44 - (23,584.84) 91,980.88

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 17
Frame Calculation - Example: 1

Structure Stiffness Matrix: [K]

35.69 81.43 81.43 35.69

14 17 20 23
1,220.00 kg/m 1,220.00 kg/m 1,220.00 kg/m
15 2 18 5 21 8 24 11
13 16 19 22
1
34.79 2
22.39 3 4 1 2 3 4
5 6 7 5 6 7
(22.39) (34.79) 3 6 9 12
1 4 7 10

[Q] = [K][D] + [Qf]

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 18
 Structure Stiffness Matrix: [K]

[Q] = [K][D] + [Qf]

3 13 14 15 16 17 18 19 20 21 22 23 24
0.00 29,478.28 16,376.82 - 14,739.14 - - - - - - - - - 3 D3 0.00
0.00 16,376.82 5.71E+06 - 16,376.82 (5.70E+06) - - - - - - - - 13 D13 0.00
0.00 - - 9.91E+05 23,584.84 - (8,063.19) 23,584.84 - - - - - - 14 D14 35.69
0.00 14,739.14 16,376.82 23,584.84 1.21E+05 - (23,584.84) 45,990.44 - - - - - - 15 D15 34.79
0.00 - (5.70E+06) - - 1.02E+07 - 75,818.56 (4.45E+06) - - - - - 16 D16 0.00
0.00 - - (8,063.19) (23,584.84) - 1.65E+06 (9,235.82) - (3,826.40) 14,349.02 - - - 17 D17 81.43
= +
0.00 - - 23,584.84 45,990.44 75,818.56 (9,235.82) 3.00E+05 - (14,349.02) 35,872.54 - - - 18 D18 22.39
0.00 - - - - (4.45E+06) - - 1.02E+07 - 75,818.56 (5.70E+06) - - 19 D19 0.00
0.00 - - - - - (3,826.40) (14,349.02) - 1.65E+06 9,235.82 - (8,063.19) 23,584.84 20 D20 81.43
0.00 - - - - - 14,349.02 35,872.54 75,818.56 9,235.82 3.00E+05 - (23,584.84) 45,990.44 21 D21 (22.39)
0.00 - - - - - - - (5.70E+06) - - 5.71E+06 - 16,376.82 22 D22 0.00
0.00 - - - - - - - - (8,063.19) (23,584.84) - 9.91E+05 (23,584.84) 23 D23 35.69
0.00 - - - - - - - - 23,584.84 45,990.44 16,376.82 (23,584.84) 1.21E+05 24 D24 (34.79)

Solve matrix equation for [D] :

D3 0.0002 rad
D13 (2.3567E-05) m
D14 (2.8685E-05) m
D15 (0.0003) rad
D16 (2.4005E-05) m
D17 (5.4423E-05) m
=
D18 (3.0407E-05) rad
D19 (2.5388E-05) m
D20 (5.4123E-05) m
D21 4.4025E-05 rad
D22 (2.6132E-05) m
D23 (2.8790E-05) m
D24 0.0003 rad

Page 19
Frame Calculation - Example: 1

Member #1

28.19
14
+∞
2
15 2.50
1 13 1 1
3 6.74 +∞
1
Member Fixed-End Forces 0.00 Global Memeber Force

[q]1 = [k]1 [d]1 + [qF]1

1 2 3 13 14 15
q1 12,130.98 - (16,376.82) (12,130.98) - (16,376.82) 1 - 0.00
q2 - 9.83E+05 - - (9.83E+05) - 2 - 0.00
q3 = (16,376.82) - 29,478.28 16,376.82 - 14,739.14 3 0.0002 + 0.00
q13 (12,130.98) - 16,376.82 12,130.98 - 16,376.82 13 (2.3567E-05) 0.00
q14 - (9.83E+05) - - 9.83E+05 - 14 (2.8685E-05) 0.00
q15 (16,376.82) - 14,739.14 16,376.82 - 29,478.28 15 (0.0003) 0.00

2.50 kN 28.19 kN
28.19 kN Transform to Local Member Force (2.50) kN

= 0.00 kN-m = 0.00 kN-m

T
(2.50) kN [q'] = [T] [q] (28.19) kN
(28.19) kN 2.50 kN
(6.74) kN-m (6.74) kN-m

(28.19)
28.19

2.50
5
(6.74) (2.50)
1
0.00

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 20
Frame Calculation - Example: 1

Member #2

89.13
17
+∞
5
18 3.65
2 16 2 2
6 5.97 +∞
4
Member Fixed-End Forces -∞ Memeber Force
Global

[q]2 = [k]2 [d]2 + [qF]2

4 5 6 16 17 18
q4 56,161.90 - (75,818.56) (56,161.90) - (75,818.56) 4 - 0.00
q5 - 1.64E+06 - - (1.64E+06) - 5 - 0.00
q6 = (75,818.56) - 1.36E+05 75,818.56 - 68,236.70 6 - + 0.00
q16 (56,161.90) - 75,818.56 56,161.90 - 75,818.56 16 (2.4005E-05) 0.00
q17 - (1.64E+06) - - 1.64E+06 - 17 (5.4423E-05) 0.00
q18 (75,818.56) - 68,236.70 75,818.56 - 1.36E+05 18 (3.0407E-05) 0.00

3.65 kN 89.13 kN
89.13 kN Transform to Local Member Force (3.65) kN

= (3.89) kN-m = (3.89) kN-m

T
(3.65) kN [q'] = [T] [q] (89.13) kN
(89.13) kN 3.65 kN
(5.97) kN-m (5.97) kN-m

(89.13)
89.13

3.65
6
(5.97) (3.65)
2
(3.89)

Note1 Note2 Prepared by: Calculation Date:

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Page 21
Frame Calculation - Example: 1

Member #3

88.64
20
+∞
8
21 1.91
3 19 3 3
9 4.08 -∞
7
Member Fixed-End Forces Global Memeber +∞
Force

[q]3 = [k]3 [d]3 + [qF]3

7 8 9 19 20 21
q7 56,161.90 - (75,818.56) (56,161.90) - (75,818.56) 7 - 0.00
q8 - 1.64E+06 - - (1.64E+06) - 8 - 0.00
q9 = (75,818.56) - 1.36E+05 75,818.56 - 68,236.70 9 - + 0.00
q19 (56,161.90) - 75,818.56 56,161.90 - 75,818.56 19 (2.5388E-05) 0.00
q20 - (1.64E+06) - - 1.64E+06 - 20 (5.4123E-05) 0.00
q21 (75,818.56) - 68,236.70 75,818.56 - 1.36E+05 21 4.4025E-05 0.00

(1.91) kN 88.64 kN
88.64 kN Transform to Local Member Force 1.91 kN

= 1.08 kN-m = 1.08 kN-m

T
1.91 kN [q'] = [T] [q] (88.64) kN
(88.64) kN (1.91) kN
4.08 kN-m 4.08 kN-m

(88.64)
88.64

(1.91)
7
4.08 1.91
3
1.08

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 22
Frame Calculation - Example: 1

Member #4

28.29
23
+∞
11
24 4.24
4 22 4 4
12 7.77 -∞
10
Member Fixed-End Forces Global Memeber Force +∞

[q]4 = [k]4 [d]4 + [qF]4

10 11 12 22 23 24
q10 12,130.98 - (16,376.82) (12,130.98) - (16,376.82) 10 - 0.00
q11 - 9.83E+05 - - (9.83E+05) - 11 - 0.00
q12 = (16,376.82) - 29,478.28 16,376.82 - 14,739.14 12 - + 0.00
q22 (12,130.98) - 16,376.82 12,130.98 - 16,376.82 22 (2.6132E-05) 0.00
q23 - (9.83E+05) - - 9.83E+05 - 23 (2.8790E-05) 0.00
q24 (16,376.82) - 14,739.14 16,376.82 - 29,478.28 24 0.0003 0.00

(4.24) kN 28.29 kN
28.29 kN Transform to Local Member Force 4.24 kN

= 3.67 kN-m = 3.67 kN-m

T
4.24 kN [q'] = [T] [q] (28.29) kN
(28.29) kN (4.24) kN
7.77 kN-m 7.77 kN-m

(28.29)
28.29

(4.24)
8
7.77 4.24
4
3.67

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 23
Frame Calculation - Example: 1

Member #5

35.69 35.69 +∞ 43.18

14 17
1,220.00 kg/m
15 18 +∞ 2.50
13 16
5 34.79 5 +∞ 5 50.61
(34.79)
Member Fixed-End Forces Global Memeber Force

[q]5 = [k]5 [d]5 + [qF]5

13 14 15 16 17 18
q13 5.70E+06 - - (5.70E+06) - - 13 (2.3567E-05) 0.00
q14 - 8,063.19 23,584.84 - (8,063.19) 23,584.84 14 (2.8685E-05) 35.69
q15 = - 23,584.84 91,980.88 - (23,584.84) 45,990.44 15 (0.0003) + 34.79
q16 (5.70E+06) - - 5.70E+06 - - 16 (2.4005E-05) 0.00
q17 - (8,063.19) (23,584.84) - 8,063.19 (23,584.84) 17 (5.4423E-05) 35.69
q18 - 23,584.84 45,990.44 - (23,584.84) 91,980.88 18 (3.0407E-05) (34.79)

2.50 kN
28.19 kN

= 6.74 kN-m
(2.50) kN
43.18 kN
(50.61) kN-m

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 24
Frame Calculation - Example: 1

Member #6

45.75 45.75 +∞ 45.56

17 20
1,220.00 kg/m
18 21 +∞ 6.15
16 19
6 57.19 6 +∞ 6 55.12
(57.19)
Member Fixed-End Forces Global Memeber Force

[q]6 = [k]6 [d]6 + [qF]6

16 17 18 19 20 21
q16 4.45E+06 - - (4.45E+06) - - 16 (2.4005E-05) 0.00
q17 - 3,826.40 14,349.02 - (3,826.40) 14,349.02 17 (5.4423E-05) 45.75
q18 = - 14,349.02 71,745.09 - (14,349.02) 35,872.54 18 (3.0407E-05) + 57.19
q19 (4.45E+06) - - 4.45E+06 - - 19 (2.5388E-05) 0.00
q20 - (3,826.40) (14,349.02) - 3,826.40 (14,349.02) 20 (5.4123E-05) 45.75
q21 - 14,349.02 35,872.54 - (14,349.02) 71,745.09 21 4.4025E-05 (57.19)

6.15 kN
45.94 kN

= 56.58 kN-m
(6.15) kN
45.56 kN
(55.12) kN-m

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 25
Frame Calculation - Example: 1

Member #7

35.69 35.69 +∞ 28.29

20 23
1,220.00 kg/m
21 24 +∞ 4.24
19 22
7 34.79 7 +∞ 7 7.77
(34.79)
Member Fixed-End Forces Global Memeber Force

[q]7 = [k]7 [d]7 + [qF]7

19 20 21 22 23 24
q19 5.70E+06 - - (5.70E+06) - - 19 (2.5388E-05) 0.00
q20 - 8,063.19 23,584.84 - (8,063.19) 23,584.84 20 (5.4123E-05) 35.69
q21 = - 23,584.84 91,980.88 - (23,584.84) 45,990.44 21 4.4025E-05 + 34.79
q22 (5.70E+06) - - 5.70E+06 - - 22 (2.6132E-05) 0.00
q23 - (8,063.19) (23,584.84) - 8,063.19 (23,584.84) 23 (2.8790E-05) 35.69
q24 - 23,584.84 45,990.44 - (23,584.84) 91,980.88 24 0.0003 (34.79)

4.24 kN
43.08 kN

= 51.04 kN-m
(4.24) kN
28.29 kN
(7.77) kN-m

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 26
Frame Calculation - Example: 1

Frame's Reactions

1,220.00 kg/m 1,220.00 kg/m 1,220.00 kg/m

5 6 7 8
5 6 7
1 389.492 kg-m 107.923kg-m 367.294kg-m
2.70 m

249.80 kg 365.36 kg 191.20 kg 423.95 kg

1 2 3 4

2,818.64 kg 8,912.78 kg 8,863.68 kg 2,828.89 kg

5.85 m 7.50 m 5.85 m

Equilibrium check:
+ sum Fx = 0, + 2.50 + 3.65 - 1.91 - 4.24 = (0.0000) kN OK
+
sum Fy = 0, + 28.19 + 89.13 + 88.64 + 28.29 - 71.37 - 91.50 - 71.37 = (0.0000) kN OK

+ sum Mz = 0, - 3.89 + (89.13)(5.85) + 1.08 + (88.64)(13.35) + 3.67 + (28.29)(19.20) -

(@ node #1) (71.37)(2.92) - (91.50)(9.60) - (71.37)(16.27) = (0.0000) kN-m OK

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 27
Frame Calculation - Example: 1

S.F.D. (kg)

4,594.43 4,308.11
2,818.64

(249.80) (365.36) 191.20 423.95

5 6 7
1 2 3 (2,828.89)
4
(4,318.36) (4,555.57)
(249.80) (365.36) 191.20 423.95

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 28
Frame Calculation - Example: 1

B.M.D. (kg-m)

2,581.06 2,664.32 2,502.12

(674.45)
(674.45) (596.98) 408.33 777.38
(777.38)

5 (5,061.12)
(5,658.09) 6 (5,104.07)
(5,512.40) 7
1 2 3 4

389.49 (107.92) (367.29)

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 29
Frame Calculation - Example: 1

Frame Deformation (mm)

5 6 7 8
5 6 7
1 2 3 4

1 2 3 4

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 30
Frame Calculation - Example: 1

Node's Reactions & Deflections

node type Rx Ry Mz disp-x disp-y rotation
(kg) (kg) (kg-m) (mm) (mm) (rad)
1 249.80 2,818.64 0.00 0.00 0.00 0.00
2 365.36 8,912.78 (389.49) 0.00 0.00 0.00
3 (191.20) 8,863.68 107.92 0.00 0.00 0.00
4 (423.95) 2,828.89 367.29 0.00 0.00 0.00
5 0.00 0.00 0.00 (0.02) (0.03) (0.00)
6 0.00 0.00 0.00 (0.02) (0.05) (0.00)
7 0.00 0.00 0.00 (0.03) (0.05) 0.00
8 0.00 0.00 0.00 (0.03) (0.03) 0.00

Member's End Forces

member Axial Force Shear Moment Axial Force Shear Moment
(kg) (kg) (kg-m) (kg) (kg) (kg-m)
1 2,818.64 (249.80) 0.00 (2,818.64) 249.80 (674.45)
2 8,912.78 (365.36) (389.49) (8,912.78) 365.36 (596.98)
3 8,863.68 191.20 107.92 (8,863.68) (191.20) 408.33
4 2,828.89 423.95 367.29 (2,828.89) (423.95) 777.38
5 249.80 2,818.64 674.45 (249.80) 4,318.36 (5,061.12)
6 615.15 4,594.43 5,658.09 (615.15) 4,555.57 (5,512.40)
7 423.95 4,308.11 5,104.07 (423.95) 2,828.89 (777.38)

Section Forces & Displacement : Member 1

section @ position disp-x disp-y rotation-z Axial Force Shear Force Moment
no (m) (mm) (mm) radian (kg) (kg) (kg-m)
1 0.00 0.00 0.00 0.00 2,818.64 (249.80) (0.00)
2 0.54 (0.08) (0.01) 0.00 2,818.64 (249.80) (134.89)
3 1.08 (0.15) (0.01) 0.00 2,818.64 (249.80) (269.78)
4 1.62 (0.17) (0.02) (0.00) 2,818.64 (249.80) (404.67)
5 2.16 (0.14) (0.02) (0.00) 2,818.64 (249.80) (539.56)
6 2.70 (0.02) (0.03) (0.00) 2,818.64 (249.80) (674.45)

Section Forces & Displacement : Member 2

section @ position disp-x disp-y rotation-z Axial Force Shear Force Moment
no (m) (mm) (mm) radian (kg) (kg) (kg-m)
1 0.00 0.00 0.00 0.00 8,912.78 (365.36) 389.49
2 0.54 (0.01) (0.01) 0.00 8,912.78 (365.36) 192.20
3 1.08 (0.02) (0.02) 0.00 8,912.78 (365.36) (5.10)
4 1.62 (0.03) (0.03) 0.00 8,912.78 (365.36) (202.39)

Note1 Note2 Prepared by: Calculation Date:

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Page 31
Frame Calculation - Example: 1

Section Forces & Displacement : Member 2

section @ position disp-x disp-y rotation-z Axial Force Shear Force Moment
no (m) (mm) (mm) radian (kg) (kg) (kg-m)
5 2.16 (0.03) (0.04) (0.00) 8,912.78 (365.36) (399.68)
6 2.70 (0.02) (0.05) (0.00) 8,912.78 (365.36) (596.98)

Section Forces & Displacement : Member 3

section @ position disp-x disp-y rotation-z Axial Force Shear Force Moment
no (m) (mm) (mm) radian (kg) (kg) (kg-m)
1 0.00 0.00 0.00 0.00 8,863.68 191.20 (107.92)
2 0.54 0.00 (0.01) (0.00) 8,863.68 191.20 (4.67)
3 1.08 0.00 (0.02) (0.00) 8,863.68 191.20 98.58
4 1.62 0.00 (0.03) 0.00 8,863.68 191.20 201.83
5 2.16 (0.01) (0.04) 0.00 8,863.68 191.20 305.08
6 2.70 (0.03) (0.05) 0.00 8,863.68 191.20 408.33

Section Forces & Displacement : Member 4

section @ position disp-x disp-y rotation-z Axial Force Shear Force Moment
no (m) (mm) (mm) radian (kg) (kg) (kg-m)
1 0.00 0.00 0.00 0.00 2,828.89 423.95 (367.29)
2 0.54 0.02 (0.01) (0.00) 2,828.89 423.95 (138.36)
3 1.08 0.06 (0.01) (0.00) 2,828.89 423.95 90.58
4 1.62 0.09 (0.02) (0.00) 2,828.89 423.95 319.51
5 2.16 0.07 (0.02) 0.00 2,828.89 423.95 548.44
6 2.70 (0.03) (0.03) 0.00 2,828.89 423.95 777.38

Section Forces & Displacement : Member 5

section @ position disp-x disp-y rotation-z Axial Force Shear Force Moment
no (m) (mm) (mm) radian (kg) (kg) (kg-m)
1 0.00 (0.02) (0.03) (0.00) 249.80 2,818.64 (674.45)
2 1.17 (0.02) (0.36) (0.00) 249.80 1,391.24 1,788.33
3 2.34 (0.02) (0.53) (0.00) 249.80 (36.16) 2,581.06
4 3.51 (0.02) (0.44) 0.00 249.80 (1,463.56) 1,703.72
5 4.68 (0.02) (0.20) 0.00 249.80 (2,890.96) (843.67)
6 5.85 (0.02) (0.05) (0.00) 249.80 (4,318.36) (5,061.12)

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
Page 32
Frame Calculation - Example: 1

Section Forces & Displacement : Member 6

section @ position disp-x disp-y rotation-z Axial Force Shear Force Moment
no (m) (mm) (mm) radian (kg) (kg) (kg-m)
1 0.00 (0.02) (0.05) (0.00) 615.15 4,594.43 (5,658.09)
2 1.50 (0.02) (0.40) (0.00) 615.15 2,764.43 (138.96)
3 3.00 (0.02) (0.81) (0.00) 615.15 934.43 2,635.18
4 4.50 (0.02) (0.81) 0.00 615.15 (895.57) 2,664.32
5 6.00 (0.03) (0.41) 0.00 615.15 (2,725.57) (51.54)
6 7.50 (0.03) (0.05) 0.00 615.15 (4,555.57) (5,512.40)

Section Forces & Displacement : Member 7

section @ position disp-x disp-y rotation-z Axial Force Shear Force Moment
no (m) (mm) (mm) radian (kg) (kg) (kg-m)
1 0.00 (0.03) (0.05) 0.00 423.95 4,308.11 (5,104.07)
2 1.17 (0.03) (0.18) (0.00) 423.95 2,880.71 (898.62)
3 2.34 (0.03) (0.42) (0.00) 423.95 1,453.31 1,636.78
4 3.51 (0.03) (0.50) 0.00 423.95 25.91 2,502.12
5 4.68 (0.03) (0.34) 0.00 423.95 (1,401.49) 1,697.40
6 5.85 (0.03) (0.03) 0.00 423.95 (2,828.89) (777.38)

Note1 Note2 Prepared by: Calculation Date:

Engineering Clinic Design and Construction Surasak Ngamsanit Aug 26, 2560 BE
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