REPUBLIC OF THE PHILIPPINES

NUEVA ECIJA UNIVERSITY OF SCIENCE AND TECHNOLOGY

CABANATUAN CITY

COLLEGE OF ENGINEERING

CE 514 Structural Steel Design

LABORATORY NO. 1

STRESSES ON TRUSS

Submitted by:

Desireine Louise A. Jacinto

Sem Lenard L. Villajuan

BSCE 5-B

Submitted to:

Engr. Roselle C. Gonzales

Subject Instructor
Date Submitted : December 10, 2020
CE 514 Structural Steel Design
Laboratory No. 1

Title : Stresses on Truss

Determine stress on truss members using graphical method (Maxwell’s Diagram)

General Data
1.1 Length -------------------------------- L varies as per floor plan design
1.2 Pitch ---------------------------------- L/5
1.3 Bay Length -------------------------- 6 m ( may varies)
1.4 Right end roller support; Left end hinged support
a. Use corrugated asbestos whose thickness is 1/3 inch for roof covering
b. Assume weight of purlins to be 200 Pa
c. Weight of truss : use formula : W = 35.9 [ 1 + (L1/3.048)]
d. Assume weight of bracing = 90 Pa
e. Assume weight of ceiling = 80 Pa
f. Assume weight of ceiling joist = 150 Pa
f.1 Assume velocity of wind to be 60m/s
f.2 Assume live load to be 1200 Pa
GIVEN:
L (LENGTH) = 9.5 m BL (BAY LENGTH) = 6 m
𝐿 9.5
PITCH = = = 1.9 m
5 5

BY PYTHAGOREAN THEOREM:

𝑦
Z2 = 1.902 + 4.752 tan 𝜃 = 𝑥
1.90
Z = 5.12 m 𝜃 = tan−1 (4.75)
𝑍 5.12
4
= 4
= 1.28 m 𝜃 = 21.80 °

𝑍 5.12
( ) ( )
4 4
X1 = = = 1.38 m
cos 𝜃 cos 21.80°

X2 = L – 4 (X1)
X2 = 9.5 – 4 (1.38) = 3.98 m

𝑧
X3 = 4
cos 𝜃
5.12
X3 = 4
cos 21.80° = 1.188 m
TRIBUTARY AREAS:
𝑍
TARS = 4 (𝐵𝐿) TAVS = 𝑋3 (𝐵𝐿)
5.12
TARS = (6) = 7.68 m2 TAVS = (1.188) (6) = 7.128 m2
4

1
TA1 = 𝑋1 (𝐵𝐿) TA2 = (𝑋1 + 𝑋2 ) (𝐵𝐿)
2
TA1 = (1.38) (6) = 8.28 m2 TA2 = 16.08 m2

𝐿
WT = 35.9 ( 1 + 3.048 )
9.5
WT = 35.9 ( 1 + 3.048 ) = 147.793 Pa

DEAD LOAD ON TOP CHORD:

1
DL ON TC = (192 + 200 + 90) (𝑇𝐴𝑅𝑆) + 2 (𝑊𝑇 )(𝑇𝐴𝑉𝑆)
1
= (192 + 200 + 90)(7.68) + 2 (147.793)(7.128)
𝑁 𝐾𝑁
DL 0N TC = 4228.49 𝑃𝑃 ≈ 4.89 𝑃𝑃

DEAD LOAD ON BOTTOM CHORD:

1
DL ON BC = (80 + 150)(𝑇𝐴1 ) + 2 (𝑊𝑇 )(𝑇𝐴1 )
1
= (80 + 150)(8.28) + 2 (147.793)(8.28)
𝑁 𝐾𝑁
DL ON BC = 2516.26 𝑃𝑃 ≈ 2.52 𝑃𝑃

1
DL ON BC = (80 + 150)(𝑇𝐴2 ) + 2 (𝑊𝑇 )(𝑇𝐴2 )
1
= (80 + 150)(16.08) + 2 (147.793)(16.08)
𝑁 𝐾𝑁
DL ON BC = 4886.66 𝑃𝑃
≈ 4.89 𝑃𝑃

LIVE LOAD ON TOP CHORD:

LL ON TC = 1200 (𝑇𝐴𝑉𝑆)
= 1200 (7.128)
𝑁 𝐾𝑁
LL ON TC = 8553.6 𝑃𝑃 ≈ 8.55 𝑃𝑃
WIND LOAD:

P = 0.766 𝑉 2 ; V = 60 m/s
= 0.766 (60)2
P = 2757.6

2 sin 𝜃
Pn = 𝑃 [1+ sin2 𝜃]
2 sin 21.80°
= 2757.6 [1+ sin2 21.80°]
Pn = 1799.93 𝑃𝑎

WL = 𝑃𝑛 (𝑇𝐴𝑉𝑆)
= 1799.93 (7.68)
𝑁 𝐾𝑁
WL = 13823.46 𝑃𝑃 ≈ 13.83 𝑃𝑃

WLL = 13.82 𝐾𝑁
WLR = 13.82 𝐾𝑁
DEAD LOAD ON TOP CHORD

∑MLo = 0
𝑅𝐿𝑜 (9.5) = 2.115(9.5) + 4.32(8.316 + 7.128 + 5.94 + 4.752 + 3.564 + 2.376 + 1.188)
𝑅𝐿𝑜 = 16.9 𝐾𝑁

∑Fv = 0
𝑅𝐿′𝑜 + 16.9 + 2(2.115) + 7(4.23) = 0
𝑅𝐿′𝑜 = 16.9 𝐾𝑁
DEAD LOAD ON TOP CHORD
TABULATION:

MEMBERS Diag. NAME LENGTH STRESS (KN) REMARKS

L0U1 a-1 19 40.19 C

U1U2 b-2 18.3 38.70 C
U2U3 c-5 17.6 37.22 C
U3U4 d-6 16.8 35.53 C
U4U'3 e-8 16.8 35.53 C
U'3U'2 f-9 17.6 37.22 C
U'2U'1 g-12 18.1 38.28 C
U'1L'o h-13 19 40.19 C
LoL1 1-j 17.7 37.44 T
L1L2 3-j 15 31.73 T
L2L'2 7-j 9.9 20.94 T
L'2L'1 11-j 15 31.73 T
L'1L'o 13-j 17.7 37.44 T
U1L1 2-1 1.9 4.02 C
U2L1 3 -2 2.5 5.29 T
U2L2 4-3 3.7 7.83 C
U2m 5-4 2.7 5.71 T
L2m 4-7 5.2 11.00 T
U3m 6-5 1.9 4.02 C
U4m 7-6 7.8 16.50 T
U4n 8-7 7.8 16.50 T
U'3n 9-8 1.9 4.02 C
L'2n 7-10 5.0 10.58 T
U'2n 10-9 2.7 5.71 T
U'2L'2 11-10 3.7 7.83 C
U'2L'1 12-11 2.5 5.28 T
U'1L'1 13-12 1.9 4.02 C
LIVE LOAD ON TOP CHORD

∑MLo = 0
𝑅𝐿𝑜 (9.5) = 4.275(9.5) + 8.55(8.316 + 7.128 + 5.94 + 4.752 + 3.564 + 2.376 + 1.188)
𝑅𝐿𝑜 = 34.2 𝐾𝑁

∑Fv = 0
𝑅𝐿′𝑜 + 34.2 + 2(4.275) + 7(8.55) = 0
𝑅𝐿′𝑜 = 34.2 𝐾𝑁
LIVE LOAD ON TOP CHORD
TABULATION:

MEMBERS Diag. NAME LENGTH STRESS (KN) REMARKS

L0U1 a-1 19 81.23 C

U1U2 b-2 18.3 78.23 C
U2U3 c-5 17.6 75.24 C
U3U4 d-6 16.8 71.82 C
U4U'3 e-8 16.8 71.82 C
U'3U'2 f-9 17.6 75.24 C
U'2U'1 g-12 18.3 78.23 C
U'1L'o h-13 19 81.23 C
LoL1 1-j 17.2 73.53 T
L1L2 3-j 15.1 64.55 T
L2L'2 7-j 10.1 43.18 T
L'2L'1 11-j 15.1 64.55 T
L'1L'o 13-j 17.2 73.53 T
U1L1 2-1 1.9 8.12 C
U2L1 3 -2 2.6 11.12 T
U2L2 4-3 3.7 15.82 C
U2m 5-4 2.6 11.12 T
L2m 4-7 5.0 21.38 T
U3m 6-5 1.9 8.12 C
U4m 7-6 7.6 32.49 T
U4n 8-7 7.6 32.49 T
U'3n 9-8 1.9 8.12 C
L'2n 7-10 5.0 21.38 T
U'2n 10-9 2.6 11.12 T
U'2L'2 11-10 3.7 15.82 C
U'2L'1 12-11 2.6 11.12 T
U'1L'1 13-12 1.9 8.12 C
DEAD LOAD ON BOTTOM CHORD

∑ML’o = 0
𝑅𝐿𝑜 (9.5) = 2.52(8.119 + 1.379) + 4.89(6.74 + 2.759)
𝑅𝑙𝑜 = 7.41 𝐾𝑁

∑Fv = 0
7.41 − 2.52(2) − 4.89(2) + 𝑅𝐿′ 𝑜 = 0
𝑅𝐿′𝑜 = 7.41 𝐾𝑁
DEAD LOAD ON BOTTOM CHORD
TABULATION:

MEMBERS Diag. NAME LENGTH STRESS (KN) REMARKS

L0U1 a-1 16 20.16 C

U1U2 b-2 16 20.16 C
U2U3 c-5 13.2 16.63 C
U3U4 d-6 13.2 16.63 C
U4U'3 e-8 13.2 16.23 C
U'3U'2 f-9 13.2 16.23 C
U'2U'1 g-12 16 20.16 C
U'1L'o h-13 16 20.16 C
LoL1 1-j 14.8 18.65 T
L1L2 3-j 12.8 16.13 T
L2L'2 7-j 8 10.08 T
L'2L'1 11-j 12.8 16.13 T
L'1L'o 13-j 14.8 18.65 T
U1L1 2-1 - - C
U2L1 3 -2 3.0 3.78 T
U2L2 4-3 1.0 1.26 C
U2m 5-4 - - T
L2m 4-7 7.0 8.82 T
U3m 6-5 - - C
U4m 7-6 7.0 8.82 T
U4n 8-7 7.0 8.82 T
U'3n 9-8 - - C
L'2n 7-10 7.0 8.82 T
U'2n 10-9 - - T
U'2L'2 11-10 1.0 1.26 C
U'2L'1 12-11 3.0 3.78 T
U'1L'1 13-12 - - C
WIND LOAD LEFT

∑ MLo = 0
𝑅𝐿′𝑜 (9.5) = 6.91(1.28)(4) + 13.82(2)(3)
𝑅𝐿′𝑜 = 12.45 𝐾𝑁

∑Fx = 0
𝑅𝐿𝑜𝑥 = 13.82(4) sin 21.80°
𝑅𝐿𝑜𝑥 = 20.53 𝐾𝑁

∑Fy = 0
𝑅𝐿𝑜𝑦 = [4(13.82) cos 21.80°] − 12.45
𝑅𝐿𝑜𝑦 = 38.88 𝐾𝑁
WIND LOAD LEFT
TABULATION:

MEMBERS Diag. NAME LENGTH STRESS (KN) REMARKS

L0U1 a-1 11.80 81.54 C

U1U2 b-2 11.80 81.54 C
U2U3 c-5 11.80 81.54 C
U3U4 d-6 11.80 81.54 C
U4U'3 e-8 5.70 39.39 C
U'3U'2 f-9 5.70 39.39 C
U'2U'1 g-12 5.70 39.39 C
U'1L'o h-13 5.70 39.39 C
LoL1 1-j 13.60 93.98 T
L1L2 3-j 10.80 74.63 T
L2L'2 7-j 5.20 35.94 T
L'2L'1 11-j 5.20 35.94 T
L'1L'o 13-j 5.20 35.94 T
U1L1 2-1 2.0 13.82 C
U2L1 3 -2 2.80 19.35 T
U2L2 4-3 4.0 27.64 C
U2m 5-4 2.80 19.35 T
L2m 4-7 5.20 35.93 T
U3m 6-5 2.0 13.82 C
U4m 7-6 8.20 56.66 T
U4n 8-7 - - -
U'3n 9-8 - - -
L'2n 7-10 - - -
U'2n 10-9 - - -
U'2L'2 11-10 - - -
U'2L'1 12-11 - - -
U'1L'1 13-12 - - -
WIND LOAD RIGHT

∑ ML’o = 0
𝑅𝐿𝑜𝑦 (9.5) = 6.91(1.28)(4) + 13.82(2)(3)
𝑅𝐿𝑜𝑦 = 12.45 𝐾𝑁

∑Fx = 0
𝑅𝐿𝑜𝑥 = 13.82(4) sin 21.80°
𝑅𝐿𝑜𝑥 = 20.53 𝐾𝑁

∑Fy = 0
𝑅𝐿′𝑜 = [4(13.82) cos 21.80°] − 12.45
𝑅𝐿′𝑜 = 38.88 𝐾𝑁
WIND LOAD RIGHT
TABULATION:

MEMBERS Diag. NAME LENGTH STRESS (KN) REMARKS

L0U1 a-1 5.80 40.08 C

U1U2 b-2 5.80 40.08 C
U2U3 c-5 5.80 40.08 C
U3U4 d-6 5.80 40.08 C
U4U'3 e-8 12.0 82.92 C
U'3U'2 f-9 12.0 82.92 C
U'2U'1 g-12 12.0 82.92 C
U'1L'o h-13 12.0 82.92 C
LoL1 1-j 2.40 16.58 T
L1L2 3-j 2.40 16.58 T
L2L'2 7-j 2.40 16.58 T
L'2L'1 11-j 8.0 55.28 T
L'1L'o 13-j 10.60 73.25 T
U1L1 2-1 - - -
U2L1 3 -2 - - -
U2L2 4-3 - - -
U2m 5-4 - - -
L2m 4-7 - - -
U3m 6-5 - - -
U4m 7-6 - - -
U4n 8-7 8.30 53.35 T
U'3n 9-8 2.0 13.82 C
L'2n 7-10 5.60 38.70 T
U'2n 10-9 2.70 18.66 T
U'2L'2 11-10 4.0 27.64 C
U'2L'1 12-11 2.70 18.66 T
U'1L'1 13-12 2.0 13.82 C
LOAD COMBINATION:

MEMBER DC ON DL ON BC LL ON WL WR 1+2+3 1+2+4 1+2+5 DESIGNING RE

TC (2) TC (4) (5) STRESS MA
(1) (3) RKS
L0U1 40.19 20.16 81.23 81.54 40.08 141.58 141.89 100.43 141.89 C
U1U2 38.70 20.16 78.23 81.54 40.08 137.09 140.40 98.94 140.40 C
U2U3 37.22 16.63 75.24 81.54 40.08 129.09 135.39 93.93 135.39 C
U3U4 35.53 16.63 71.82 81.54 40.08 123.98 133.70 92.94 133.70 C
U4U'3 35.53 16.23 71.82 39.39 82.92 123.58 91.15 134.68 134.68 C
U'3U'2 37.22 16.23 75.24 39.39 82.92 128.69 92.84 136.37 136.37 C
U'2U'1 38.28 20.16 78.23 39.39 82.92 136.67 97.84 141.36 141.36 C
U'1L'o 40.19 20.16 81.23 39.39 82.92 141.58 99.74 143.27 143.27 C
LoL1 37.44 18.65 73.53 93.98 16.58 129.62 150.07 72.67 150.07 T
L1L2 31.73 16.13 64.55 74.63 16.58 112.41 128.49 64.44 128.49 T
L2L'2 20.94 10.08 43.18 35.94 16.58 74.20 66.69 47.60 74.20 T
L'2L'1 31.73 16.13 64.55 35.94 55.28 112.41 83.90 103.14 112.41 T
L'1L'o 37.44 18.65 73.53 35.94 73.25 129.62 92.03 129.34 129.62 T
U1L1 4.02 - 8.12 13.82 - 12.14 17.84 4.02 17.84 C
U2L1 5.29 3.78 11.12 19.35 - 20.19 28.42 9.07 28.42 T
U2L2 7.83 1.26 15.82 27.64 - 24.91 36.73 9.09 36.73 C
U2m 5.71 - 11.12 19.35 - 16.83 25.06 5.71 25.06 T
L2m 11.00 8.82 21.38 35.93 - 41.20 55.75 19.82 55.75 T
U3m 4.02 - 8.12 13.82 - 12.14 17.84 4.02 17.84 C
U4m 16.50 8.82 32.49 56.66 - 57.81 81.98 25.32 81.98 T
U4n 16.50 8.82 32.49 - 53.35 57.81 25.32 78.67 78.67 T
U'3n 4.02 - 8.12 - 13.82 12.14 4.02 17.82 17.82 C
L'2n 10.58 8.82 21.38 - 38.70 40.78 19.40 58.10 58.10 T
U'2n 5.71 - 11.12 - 18.66 16.83 5.71 24.37 24.37 T
U'2L'2 7.83 1.26 15.82 - 27.64 24.91 9.09 36.73 36.73 C
U'2L'1 5.28 3.78 11.12 - 18.66 20.18 9.06 27.72 27.72 T
U'1L'1 4.02 - 8.12 - 13.82 12.14 4.02 17.84 17.84 C