Name: CRISELLE ANNE D.

BALDOZA Date: 12/12/2022

Instructor: ENGR. EDNA P. MONTAÑEZ Year & Section: 4B

Horizontal Distribution of Lateral Forces

The Typical Floor Plan

Base Shear and Lateral Forces of the Building

Frame elevation along Grids A, B and C

Frame elevation along Grids 1, 2 and 3

Deflection & Stiffness along X-Direction

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌𝑨 =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
A A1 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
A2 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
A3 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
A4 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
A5 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
A6 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
A7 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 156.50

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4 𝟏
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉
𝒌B =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
B B1 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
B3 0.4X0.4 3 0.16 0.002133 0.042459 0.002117 0.044576 22.43
B4 0.4X0.4 3 0.16 0.002133 0.042459 0.002117 0.044576 22.43
B5 0.4X0.4 3 0.16 0.002133 0.042459 0.002117 0.044576 22.43
B7 0.4X0.4 3 0.16 0.002133 0.042459 0.002117 0.044576 22.43
SUM = 112.09

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌C =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
C C1 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
C2 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
C3 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
C5 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
C6 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
C7 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 134.15

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4 𝟏
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉
𝒌D =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
D D1 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
D2 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
D3 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
D4 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
D5 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
D6 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
D7 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 156.50
 Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness
2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌E =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
E E1 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
E2 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
E4 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
E6 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
E7 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 111.79

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌F =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
F F1 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
F2 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
F3 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
F4 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
F5 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
F6 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
F7 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 156.50

Deflection & Stiffness along Y-Direction

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌𝟏 =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
1 1A 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
1B 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
1C 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
1D 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
1E 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
1F 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 134.15

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌2 =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
2 2A 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
 2C 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
2D 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
2E 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
2F 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 111.79

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌3 =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
3 3A 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
3B 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
3C 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
3D 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
3F 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 111.79

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌4 =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
4 4A 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
4B 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
4D 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
4E 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
4F 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 111.79

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌5 =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
5 5A 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
5B 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
5C 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
5D 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
5F 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 111.79

Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness

2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌6 =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
6 6A 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
6C 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
6D 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
6E 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
6F 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 111.79
 Frame Col bxd Height Area I 𝜹𝒇 = 𝜹𝑽 = Total 𝜹 Stiffness
2 4
(m) (m) (m ) (m ) 𝑷𝒉𝟑 𝟏. 𝟐𝑷𝒉 𝟏
𝒌7 =
𝟏𝟐𝑬𝒄𝑰 𝑮𝑨 𝜹
7 7A 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
7B 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
7C 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
7D 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
7E 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
7F 0.4X0.4 3 0.16 0.002133 0.042459 0.002268 0.044727 22.36
SUM = 134.15

Center of Mass
 𝛴 𝑀𝑥
𝑥𝑚 = = 10m 𝒇𝒓𝒐𝒎 𝒈𝒓𝒊𝒅 A
𝛴𝑀
𝛴𝑀𝑥
𝑦𝑚 = = 10m 𝒇𝒓𝒐𝒎 𝒈𝒓𝒊𝒅 7
𝛴𝑀

Center of Rigidity

(156.5 ∗ 0) + (112.09 ∗ 4) + (134.15 ∗ 8) + (156.5 ∗ 12) + (111.79 ∗ 16) + (156.5 ∗ 20)

𝑥𝑟 =
156.5 + 112.09 + 134.15 + 156.5 + 111.79 + 156.5
𝒙𝒓 = 10.05 𝒎 𝒇𝒓𝒐𝒎 𝒈𝒓𝒊𝒅 A

(134.15 ∗ 0) + (111.79 ∗ 3.5) + (111.79 ∗ 7) + (111.79 ∗ 10.5) + (111.79 ∗ 14) + (111.79 ∗ 17.5) + (134.15 ∗ 20)
𝑥𝑟 =
134.15 + 111.79 + 111.79 + 111.79 + 111.79 + 111.79 + 134.15

𝒚𝒓 = 10.34 𝒎 𝒇𝒓𝒐𝒎 𝒈𝒓𝒊𝒅 7

Calculation of eccentricity 𝒆𝒙 and 𝒆𝒚

𝑒𝑥 = (𝑥𝑟 − 𝑥𝑚) + 5%(20𝑚)

𝑒𝑥 = (10.05 − 10) + 0.05 (20)

𝒆𝒙 = 1.05 𝒎

𝑒𝑦 = (𝑦𝑟 − 𝑦𝑚) + 5%(20𝑚)

𝑒𝑦 = (10.34 − 10) + 0.05 (20)

𝒆𝒚 =1.34𝒎
Center of Rigidity

𝐽𝑟 = (134.15 𝑥 10.342 + 111.79 𝑥 6.842 + 111.79 𝑥 3.342 + 111.79 𝑥 0.342 + 111.79 𝑥

2.662 + 111.79 𝑥 6.162 + 134.15 𝑥 9.662 + 156.50 𝑥 10.052 + 112.09 𝑥 6.052 + 134.15 𝑥
2.052 + 156.50 𝑥 1.952 + 111.79 𝑥 5.952 + 156.50 𝑥 9.952)

𝐽𝑟 = 78 904.164 𝑘𝑁. 𝑚
Calculation of force Px along Grid 7

(𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟑𝟒)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟐𝟎. 𝟏 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟑𝟒)
𝑷𝟒𝒕𝒉 = + = 𝟑𝟏𝟖. 𝟐𝟖𝟕 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟑𝟒.𝟏𝟓)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟑𝟒.𝟏𝟓)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟑𝟒)
𝑷𝟑𝒓𝒅 = 𝟖𝟐𝟕.𝟐𝟓
+ 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
= 𝟐𝟑𝟖. 𝟕 𝒌𝑵
(𝟏𝟑𝟒.𝟏𝟓)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟑𝟒.𝟏𝟓)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟑𝟒)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟓𝟗. 𝟏𝟖𝟏 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒

Frame elevation along Grids 7

Calculation of force along Grid 6

(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟑𝟒)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟏𝟔. 𝟕𝟓 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟑𝟒)
𝑷𝟒𝒕𝒉 = + = 𝟐𝟔𝟓. 𝟐𝟑𝟔 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟑𝟒)
𝑷𝟑𝒓𝒅 = + = 𝟏𝟗𝟖. 𝟗𝟏𝟐 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟑𝟒)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟑𝟐. 𝟔𝟒𝟗 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
Frame elevation along Grids 6

Calculation of force along Grid 5

(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟑𝟒)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟏𝟔. 𝟕𝟓 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟑𝟒)
𝑷𝟒𝒕𝒉 = + = 𝟐𝟔𝟓. 𝟐𝟑𝟔 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟑𝟒)
𝑷𝟑𝒓𝒅 = + = 𝟏𝟗𝟖. 𝟗𝟏𝟐 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟑𝟒)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟑𝟐. 𝟔𝟒𝟗 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒

Frame elevation along Grids 5

Calculation of force along Grid 4

(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟑𝟒)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟏𝟔. 𝟕𝟓 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟑𝟒)
𝑷𝟒𝒕𝒉 = + = 𝟐𝟔𝟓. 𝟐𝟑𝟔 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟑𝟒)
𝑷𝟑𝒓𝒅 = + = 𝟏𝟗𝟖. 𝟗𝟏𝟐 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟑𝟒)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟑𝟐. 𝟔𝟒𝟗 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒

Frame elevation along Grids 4

Calculation of force along Grid 3

(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟑𝟒)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟏𝟔. 𝟕𝟓 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟑𝟒)
𝑷𝟒𝒕𝒉 = + = 𝟐𝟔𝟓. 𝟐𝟑𝟔 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟑𝟒)
𝑷𝟑𝒓𝒅 = + = 𝟏𝟗𝟖. 𝟗𝟏𝟐 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟑𝟒)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟑𝟐. 𝟔𝟒𝟗 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
Frame elevation along Grids 3

Calculation of force along Grid 2

(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟑𝟒)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟏𝟔. 𝟕𝟓 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟑𝟒)
𝑷𝟒𝒕𝒉 = + = 𝟐𝟔𝟓. 𝟐𝟑𝟔 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟑𝟒)
𝑷𝟑𝒓𝒅 = + = 𝟏𝟗𝟖. 𝟗𝟏𝟐 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟑𝟒)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟑𝟐. 𝟔𝟒𝟗 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒

Frame elevation along Grids 2

Calculation of force Px along Grid 1

(𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟑𝟒)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟐𝟎. 𝟏 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟑𝟒)
𝑷𝟒𝒕𝒉 = + = 𝟑𝟏𝟖. 𝟐𝟖𝟕 𝒌𝑵
𝟖𝟐𝟕. 𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟑𝟒.𝟏𝟓)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟑𝟒.𝟏𝟓)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟑𝟒)
𝑷𝟑𝒓𝒅 = + = 𝟐𝟑𝟖. 𝟕 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟑𝟒.𝟏𝟓)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟑𝟒.𝟏𝟓)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟑𝟒)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟓𝟗. 𝟏𝟖𝟏 𝒌𝑵
𝟖𝟐𝟕.𝟐𝟓 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒

Frame elevation along Grids 1

Calculation of force Py along Grid A

(𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟎𝟓)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟐𝟑. 𝟑𝟕 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟎𝟓)
𝑷𝟒𝒕𝒉 = + = 𝟑𝟕𝟎. 𝟎𝟕𝟖 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟓𝟔.𝟓𝟎)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟓𝟔.𝟓𝟎)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟎𝟓)
𝑷𝟑𝒓𝒅 = + = 𝟐𝟕𝟕. 𝟓𝟑𝟖 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟓𝟔.𝟓𝟎)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟓𝟔.𝟓𝟎)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟎𝟓)
𝑷𝟐𝒏𝒅 = 𝟖𝟐𝟕.𝟓𝟑
+ 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
= 𝟏𝟖𝟓. 𝟎𝟖𝟐 𝒌𝑵
Frame elevation along Grids A

Calculation of force Py along Grid B

(𝟏𝟏𝟐. 𝟎𝟗)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟏𝟐. 𝟎𝟗)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟎𝟓)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟏𝟔. 𝟕𝟑𝟗 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟐. 𝟎𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟏𝟐. 𝟎𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟎𝟓)
𝑷𝟒𝒕𝒉 = + = 𝟐𝟔𝟓. 𝟎𝟔𝟏 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟐.𝟎𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟏𝟐.𝟎𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟎𝟓)
𝑷𝟑𝒓𝒅 = + = 𝟏𝟗𝟖. 𝟕𝟖𝟏 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟏𝟐.𝟎𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟏𝟐.𝟎𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟎𝟓)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟑𝟐. 𝟓𝟔𝟏 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒

Frame elevation along Grids B

Calculation of force Py along Grid C

(𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟎𝟓)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟐𝟎. 𝟎𝟑𝟑 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟑𝟒. 𝟏𝟓)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟎𝟓)
𝑷𝟒𝒕𝒉 = + = 𝟑𝟏𝟕. 𝟐𝟐𝟕 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟑𝟒.𝟏𝟓)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟑𝟒.𝟏𝟓)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟎𝟓)
𝑷𝟑𝒓𝒅 = + = 𝟐𝟑𝟕. 𝟗𝟎𝟐 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟑𝟒.𝟏𝟓)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟑𝟒.𝟏𝟓)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟎𝟓)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟓𝟖. 𝟔𝟓 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒

Frame elevation along Grids C

Calculation of force Py along Grid D

(𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟎𝟓)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟐𝟑. 𝟑𝟕 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟎𝟓)
𝑷𝟒𝒕𝒉 = + = 𝟑𝟕𝟎. 𝟎𝟕𝟖 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟓𝟔.𝟓𝟎)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟓𝟔.𝟓𝟎)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟎𝟓)
𝑷𝟑𝒓𝒅 = + = 𝟐𝟕𝟕. 𝟓𝟑𝟖 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟓𝟔.𝟓𝟎)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟓𝟔.𝟓𝟎)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟎𝟓)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟖𝟓. 𝟎𝟖𝟐 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
Frame elevation along Grids D

Calculation of force Py along Grid E

(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟎𝟓)

𝑷𝑹𝑶𝑶𝑭 = + = 𝟏𝟔. 𝟔𝟗𝟒 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟏𝟏. 𝟕𝟗)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟎𝟓)
𝑷𝟒𝒕𝒉 = + = 𝟐𝟔𝟒. 𝟑𝟓𝟐 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟏𝟏.𝟕𝟗)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟎𝟓)
𝑷𝟑𝒓𝒅 = + = 𝟏𝟗𝟖. 𝟐𝟒𝟗 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟏𝟏.𝟕𝟗)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟎𝟓)
𝑷𝟐𝒏𝒅 = 𝟖𝟐𝟕.𝟓𝟑
+ 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
= 𝟏𝟑𝟐. 𝟐𝟎𝟕 𝒌𝑵

Frame elevation along Grids E

Calculation of force Py along Grid F

 (𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟐𝟐. 𝟐𝟑) (𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟐𝟐. 𝟐𝟑 ∗ 𝟏. 𝟎𝟓)
𝑷𝑹𝑶𝑶𝑭 = + = 𝟐𝟑. 𝟑𝟕 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟗𝟑𝟓. 𝟓𝟔) (𝟏𝟓𝟔. 𝟓𝟎)(𝟏𝟗𝟑𝟓. 𝟓𝟔 ∗ 𝟏. 𝟎𝟓)
𝑷𝟒𝒕𝒉 = + = 𝟑𝟕𝟎. 𝟎𝟕𝟖 𝒌𝑵
𝟖𝟐𝟕. 𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒. 𝟏𝟔𝟒
(𝟏𝟓𝟔.𝟓𝟎)(𝟏𝟒𝟓𝟏.𝟓𝟔) (𝟏𝟓𝟔.𝟓𝟎)(𝟏𝟒𝟓𝟏.𝟓𝟔∗𝟏.𝟎𝟓)
𝑷𝟑𝒓𝒅 = + = 𝟐𝟕𝟕. 𝟓𝟑𝟖 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒
(𝟏𝟓𝟔.𝟓𝟎)(𝟗𝟔𝟖.𝟎𝟎𝟓) (𝟏𝟓𝟔.𝟓𝟎)(𝟗𝟔𝟖.𝟎𝟎𝟓∗𝟏.𝟎𝟓)
𝑷𝟐𝒏𝒅 = + = 𝟏𝟖𝟓. 𝟎𝟖𝟐 𝒌𝑵
𝟖𝟐𝟕.𝟓𝟑 𝟕𝟖 𝟗𝟎𝟒.𝟏𝟔𝟒

Frame elevation along Grids F