This document provides calculations for the structural design of a metal roof. It includes: 1. Calculations of the roof covering weight, gutter weight, and reinforcement weight. 2. Application of the triangle theorem to calculate angles of the sloped roof. 3. Use of the method of nodes to calculate forces at each node of the roof structure. 4. Summation of all component weights to calculate the total load and load per node. 5. Calculation of horizontal wind force and distribution to nodes.

1. INSTITUTO POLITECNICO NACIONAL
ESCUELA SUPERIOR DE INGENIERIA Y
ARQUITECTURA UNIDAD TECAMACHALCO
ALUMNO: GUTIERREZ JAIMEZ IVAN
GRUPO: 7AV16
TURNO: VESPERTINO
ASIGNATURA: ESTRUCTURAS METALICAS
PROFESOR: FLORES VASCONCELOS DAVID

2. Armadura.
5.57m
38.99m
28.14m
4.00m
8.00m

3. Tθ=c.o./c.a.
Tθ1=1/3.51= 15.90°
1.-Cálculo de la cubierta de láminagalvanizada.
Peso lamina = 209.70kg/m²
Tθ2=2/3.51= 29.67°
Tθ3=3/3.51= 40.52°
Peso cubierta= AT (Peso de lámina)
Tθ4=4/3.51= 48.73°
Pc= (96.19m²)(9.70 kg/m²)(1.4)
Teorema de Pitágoras
Pc=1306.26kg.
C= √a²+b²
C= √(14.07)²+(4)²
C=14.62
2.-Peso de polines (canales)
W=33.95 kg/m²
5.57m
M=WL²/8
M=(33.95 kg/m²)(5.57)/8=
M= 131.66 kg/m²

4. S M/Fs= S 131.66 kg/m²/25.20 kg/²
S =5.22 cm²
Sy real= 5.22 > S
Diseño AHMSA
4”-2” calibre 12
Peso= 4.57 kg/m
Peso perfil= (5.57)(4.57)
Peso perfil= 25.23 kg (10) nodos superiores
Peso perfil= 250.30kg
3.-Peso de armadura.
Cuerda inferior x1= (28.14m)(1)= 28.14m
Cuerda superior x2= (14.62m)(2)= 29.24m
Montante 1
x2= (1.00m) (2)= 2.00m
Montante 2
x2= (2.00m) (2)= 4.00m
Montante 3
x2= (3.00m) (2)= 6.00m
Diagonales 1
x2= (4.03m) (2)= 8.06m
Diagonales 2
x2=(4.61m) (2)= 9.22m
Diagonales 3
x2=(5.32m) (2)= 10.64m
Total= 97.3 m
PA=(longitud de pza.)(Peso )(2)
PA= (97.3 m)(35.12)(2)
PA= 6834.35 kg
4.-Falso plafón
Peso de falso plafón=(AT)(Peso del plafón)
Pfp= (156.73m²)(100 kg/m²)
Pfp=15673kg
AT=(28.14)(5.57)
AT=156.73 m²
Área tributaria= 156.73
Peso= 100 kg/m²
5.-Carga viva.
Tabla N.T.C.E. → 100 KG/m²
Área tributaria= 96.19m²
CV= (At)(Cv)
CV=(96.19m²)(100 kg/m²)
CV=9619 kg

5. 6.-Carga de viento
W=0.00555 C A V²
C= 0.75
C= Factor de empuje (adm.)
A= 48.10
A= Área expuesta
V= 85 km/hra.
V= Velocidad de diseño
Wy
W= Fuerza debida al viento
W
W= 0.00555(0.75)(48.10)(85)²
W= 1446.56 kg
15.90°
Wy= W Senα
Wy= (1446.56)(Sen 15.90)
Wy= 357.54 kg
Wx= W Cosα
Wx= (1446.50)(Cos 15.90)
Wx= 1401.61kg x 1.4
Wx= 1962.20 kg
7.-instalaciones.
N.T.C.I. (2)→ 40kg/m²
Área tributaria= 156.73m²
P ins.= (40 kg/m²)(156.73)
P ins.= 6269 kg
8.-Peso total.
Peso de cubierta =2204.16 kg
Peso de perfil = 252.3 kg
Peso de armadura = 6834.35 kg
Peso de falso plafón = 15673 kg
Carga viva = 16230 kg
Wy =
357.54 kg
Peso de instalaciones = 6269 kg
Total.
47820.35
Factor de carga
=
x 1.4
66948.49 kg
Wx

6. 9.-Peso nodos
P.N. = PT/ Nn
P.N. = 66948.49 kg/ 8
P.N. = 8368.56 kg
10.-Peso por viento horizontal.
Pw= Wx/Nnx
Pw= 1962.26/4
Pw= 490.56 kg

7. METODO DE NODOS
RA= Ƹf/2
RA= 8 (5TON) / 2 = 40TON /2= 20 TON
NODO C
NODO A
5 TON
CD
2.5 TON
AC
15.90°
15.90°
AJ
AC
CJ
RA
ΣFy= -2.5TON+ 20TON- AC(Sen 15.90)
ΣFy= 17.5TON- AC (0.24)
AC= 17.5TON/0.24
AC= 72.91 TON
ΣFx= -72.9TON (Cos 15.90)- CD(Cos15.90)
ΣFx= 70.64- CD (Cos 15.90)
CD = 70.64/0.96
CD= 73.58 TON
ΣFx= -72.9TON(Cos 15.90) +AJ
AJ=72.9 (0.96)
AJ= 69.98 TON
ΣFy= -5TON +72.91 (Sen 15.90)- 73.58 (Sen 15.90)+CJ
ΣFy = -5TON -18.02TON+ 18.18TON + CJ
CJ= 5.16 TON

8. NODO K
NODO J
KD
CJ
JD
KE
29.67
40.52.
67
KL
KJ
AJ
JK
ΣFy= -5.16TON + JD (Sen 29.67)
ΣFy= -5.16TON+ JD (0.44)
JD = 5.16/0.44
JD = 11.72 TON
ΣFx= -69.98TON +11.72TON (Cos 29.67)+JK
ΣFx = -69.98TON + 10.47TON + JK
JK= 59.51 TON
ΣFy= -7.73TON + KE (Sen40.52)
KE= 7.73TON/0.59
KE = 13.10 TON
ΣFx= -59.51TON +13.10TON (Cos 40.52)+KL
ΣFyx= -59.51TON + 10.53TON + KL
KL= 48.98 TON
NODO E
NODO D
5 TON
5 TON
EF
DE
DE
DC
JD
DK
EK
EL
ΣFx= +73.58TON (Cos 15.90)- 11.72TON (Cos29.67)DE (Cos15.90)
ΣFx= 71.29-10.47- DE (0.96)
DE = 60.82/0.96
DE= 63.35 TON
ΣFx=63.35TON (Cos 15.90)- 13.10TON (Cos40.52)EF(Cos 15.90)
ΣFx= 61.38-10.53-EF (0-96)
EF = 50.85/0.96
EF= 52.96 TON
ΣFy= -5TON -63.35TON (Sen 15.90)+ 73.58TON
(Sen 15.90)- 11.72TON (Sen29.67) +DK
ΣFy = -5TON – 15.65TON+ 18.18TON -5.26TON + DK
DK= 7.73 TON
ΣFy= -5TON +63.35TON (Sen 15.90)- 13.10TON
(Sen 40.52)- 52.96TON (Sen 15.90+ EL
ΣFy = -5TON + 15.65TON -7.78TON-13.01TON + EL
EL= 10.22 TON

9. NODO L
LE
LF
48.73
LK
LM
ΣFy= -10.22TON + LF (Sen48.73)
LF= 10.22TON/0.69
LF= 14.81TON
ΣFx= -48.98TON + 14.81TON (Cos 48.73)+ LM
ΣFx = -48.98TON +10.67
LM= 38.31 TON