Instrucciones. Analizar el pórtico de dos plantas mostrado en la figura, emplear el Método Matricial de Compatibilidad. Considere una resistencia de concreto de 210kg/cm2.
Datos:
- Columnas: 0.25 x 0.25m
- Vigas: 0.25 x 0.50m
- Espesor de Placa: 0.25m
- μ = 0.15
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-1.png)
SOLUCION:
1. Asignar los grados de libertad y orientación de cada elemento.
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-2.png)
2. Análisis del sistema respecto al 1° GDL.
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-3.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image.png)
2. Análisis del sistema respecto al 2° GDL.
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-4.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-1.png)
2. Análisis del sistema respecto al 3° GDL.
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-5.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-2.png)
2. Análisis del sistema respecto al 4° GDL.
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-6.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-3.png)
2. Análisis del sistema respecto al 5° GDL.
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-7.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-4.png)
2. Análisis del sistema respecto al 6° GDL.
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-8.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-5.png)
2. Análisis del sistema respecto al 7° GDL.
![](https://hebmerma.com/wp-content/uploads/2022/07/MMC-E1-9.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-6.png)
3. Matriz de Compatibilidad.
![](https://hebmerma.com/wp-content/uploads/2022/07/image-7.png)
4. Matriz de Rigidez de cada elemento.
Elemento a Flexión (VIGA – COLUMNA)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-8.png)
Elemento a Corte (PLACA)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-9.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-10.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-11.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-12.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-13.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-14.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-15.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-16.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-17.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-18.png)
5. Ensamblaje de la Matriz K. K = Σ ɑₑᵀ*Kₑ*ɑₑ
![](https://hebmerma.com/wp-content/uploads/2022/07/image-19.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-20.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-21.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-22.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-23.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-24.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-25.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-26.png)
![](https://hebmerma.com/wp-content/uploads/2022/07/image-27.png)
6. Calculo de K Lateral. KLat = Kᴰᴰ – Kᴰᶿ * Kᶿᶿ⁻¹ * Kᶿᴰ