Perform torsional analysis.

B-7 Perform torsional analysis.

The load distributed to each element of the lateral load resisting system in a particular direction can be

determined by its stiffness relative to all the other elements in that direction.

The direct shear component is Fv;

Ri

Fv =

V

∑R

i

Additionally, there are two torsional components; Ftors, and Facc;

Rd i

Ftors =

where; e = eccentricity due to the displacement of the center of mass

Ve

∑

2

Rd i

to the center of rigidity

Rd i

Facc =

where; eacc = eccentricity to account for possible errors in calculating

Ve acc

∑

Rd 2

i

the cm or cr.

The shear component and the two torsional components add together to determine the total force

transferred to an element of the lateral load resisting system. Calculations for the distribution of forces to

the lateral load resisting elements at each floor level are tabularized below;

Roof;

Vtrans =

338

kips

etrans = 0 ft

etrans,acc =

8.25

ft

Vlong =

elong = 1.25 ft

elong,acc =

239

kips

2.65

ft

(1)

2

(2)

EQ

Element

Ryi

Rxi

dxi

dyi

Rxdy

Fv

Ft

Facc

Ftotal =

Direction (grid line)

or

Fv+Ft+Facc

2

Rydx

(k/ft)

(ft)

(k-ft/ft)

(kips)

Trans

A1-C1

667

-

82.5

-

55027.5

4539769

28.40

0.00

5.71

34.1

A2-B2 & 944

-

70.5

-

66552.0

4691916

40.20

0.00

6.91

47.1

(3)

C2-D2

A3-B3 &

944

-

47

-

44368.0

2085296

40.20

0.00

4.61

44.8

(3)

C3-D3

A4-B4 &

944

-

23.5

-

22184.0

521324

40.20

0.00

2.30

42.5

(3)

C4-D4

A5-B5 &

944

-

0

-

0.0

0

40.20

0.00

40.2

(3)

C5-D5

A6-B6 &

944

-

23.5

-

22184.0

521324

40.20

0.00

2.30

42.5

(3)

C6-D6

A7-B7 &

944

-

47

-

44368.0

2085296

40.20

0.00

4.61

44.8

C7-D7(3)

A8-B8 &

944

-

70.5

-

66552.0

4691916

40.20

0.00

6.91

47.1

(3)

C8-D8

A9-C9

667

-

82.5

-

55027.5

4539769 28.40

0.00

5.71

34.1

Long

A2-A8

-

2280

-

26.5

60420

1601130 119.37

0.67

1.42

121.5

D2-D8

-

2280

-

26.5

60420

1601130 119.37

-0.67

1.42

120.8

Σ Ri =

7942

4560

Jp =

26878870

1

Note: distance 'd' is measured from the cr

2

Note: only positive components are added

3

Note: there are two walls in parallel with a total rigidity of; 2 x 472-kips/ft = 944-kips/ft

Note: For metric equivalents; 1-kip/ft = 14.58KN/m, 1-ft = 0.30m, 1-kip = 4.48KN

H2-24