This document describes the calculation of moments, shear forces, and load distributions for a cross method structural design problem. Key details include: - The structure has a weight of 32.3 ton/m and dimensions of 4m x 4m x 4m - Moments are calculated at each fixed end and load point - Stiffness values are determined for each member - Load distribution factors are computed based on member stiffnesses - Shear forces are found for static and hyperstatic conditions - Moments are solved for through iterative distribution of loads and forces The full calculation is shown to solve for all member end moments, shear forces, and final reactions.

1. MÉTODO CROSS
DATOS
P = 0.00 ton I1 = 1
W = 32.30 ton/m I2 = 1
L1 = 4.00 m I3 = 1
L2 = 4.00 m E = Constante
L3 = 4.00 m
Calculo de Momentos de Empotramientos
+ MBA = 0 = 0.00 ton * m
- MBA = - (WL² / 8) = -64.60 ton * m
+ MBC = + (WL² / 12) = 43.07 ton * m
- MBC = - (WL² / 12) = -43.07 ton * m
+ MCD = + WL² / 2 = 64.60 ton * m
- MDC = 0 = 0.00 ton * m
Calculo de Rigidez de la s B arras
KBA = 3EI / L1 = 0.75 E
KBC = 4EI / L2 = 1.00 E
KCB = 4EI / L2 = 1.00 E
KCD = 3EI / L1 = 0.75 E
ΣK1 = KBA + KBC = 1.75 E
ΣK2 = KCB + KCD = 1.75 E
EDWIN DE LAO LOBERA DISEÑO ESTRUCTURAL DE CIMENTACIONES

2. Calculo de los Factores de Distribución
FDBA = KBA/(KBA+KBC) = 0.43
FDBC = KBC/(KBA+KBC) = 0.57
Σ = 1.00
FDBA = KCB/(KCB+KCD) = 0.57
FDBC = KCD/(KCB+KCD) = 0.43
Σ = 1.00
Cortante Isostático
R1 = WL / 2 = 64.6 Ton
R2 = WL / 2 = -64.6 Ton
R3 = (WL / 2) + (P / 2) = 64.6 Ton
R4 = (WL / 2) + (P / 2) = -64.6 Ton
R5 = WL / 2 = 64.6 Ton
R6 = WL / 2 = -64.6 Ton
Cortante Hiperestático
VH1 = ΣMF / L1 = -12.9261 Ton
VH2 = ΣMF / L2 = 0.0000 Ton
VH3 = ΣMF / L3 = 12.9261 Ton
Cortante Final
VF1 = V.H + V.I. = 51. 67 Ton
VF2 = V.H + V.I. = -77.53 Ton
VF3 = V.H + V.I. = 64.60 Ton
VF4 = V.H + V.I. = -64.60 Ton
VF5 = V.H + V.I. = 77.53 Ton
VF6 = V.H + V.I. = -51.67 Ton
EDWIN DE LAO LOBERA DISEÑO ESTRUCTURAL DE CIMENTACIONES

3. Calculo de los Momentos
Extremo AB
BA BC
CB CD
DC
F. Distrib.
0.43 0.57
0.57 0.43
F. Transp. 1/2.
1/2.
M. Empot. 0.00
-64.60 43.07
-43.07 64.60
0.00
M. Equil. 0.0000
21.5333
-21.5333
0.0000
1. Distr.
9.2286 12.3048
-12.3048 -9.2286
1. Transp. 4.6143
-6.1524
6.1524
-4.6143
-4.6143
6.1524
-6.1524
4.6143
2. Distr.
2.6367 3.5156
-3.5156 -2.6367
2. Transp. 1.3184
-1.7578
1.7578
-1.3184
-1.3184
1.7578
-1.7578
1.3184
3. Distr.
0.7534 1.0045
-1.0045 -0.7534
3. Transp. 0.3767
-0.5022
0.5022
-0.3767
-0.3767
0.5022
-0.5022
0.3767
4. Distr.
0.2152 0.2870
-0.2870 -0.2152
4. Transp. 0.1076
-0.1435
0.1435
-0.1076
-0.1076
0.1435
-0.1435
0.1076
5. Distr.
0.0615 0.0820
-0.0820 -0.0615
5. Transp. 0.0307
-0.0410
0.0410
-0.0307
-0.0307
0.0410
-0.0410
0.0307
Σ M. Finales 0.00
-51.70 51.70
-51.70 51.70
0.00
V.I. 64.60
-64.60 64.60
-64.60 64.60
-64.60
V.H -12.93
-12.93 0.00
0.00 12.93
12.93
Reacciones 51.67
-77.53 64.60
-64.60 77.53
-51.67
R. Final 51.67
142.13
142.13
51.67
EDWIN DE LAO LOBERA DISEÑO ESTRUCTURAL DE CIMENTACIONES