Soluciones de ejercicios de Análisis Estructural I: Líneas de influencia de momentos, Ejercicios de Análisis Estructural

¡Descarga Soluciones de ejercicios de Análisis Estructural I: Líneas de influencia de momentos y más Ejercicios en PDF de Análisis Estructural solo en Docsity! Structural Analysis I Moment Influence Line Exercise Problem Solutions Dr. Structure P a g e | 1 Problem 1: Draw the moment influence line for points A, B, and C. Then calculate the maximum positive and negative moments at each point. The beam is subjected to a moving load of 50 kN. Solution: A B C 8m 4m 4m 4m 4m A B C 8m 4m 4m 4m 4m - + - Influence line for bending moment at A Influence line for bending moment at B Influence line for bending moment at C Structural Analysis I Moment Influence Line Exercise Problem Solutions Dr. Structure P a g e | 2 Since the influence line for bending moment at A does not have a positive region, no positive moment develops at A due to the moving load. To determine the maximum negative moment at A, we can place the moving load on the beam where the influence line peaks, as shown below. We then analyze the beam to determine the magnitude of maximum negative moment at A. Using the free-body diagram of the left segment of the beam, we can easily calculate the maximum negative bending moment at A. It equals (8 m)(50 kN) 400 kN.m= To determine the maximum positive moment at B, we can place the moving load on the beam where the influence line peaks, as shown below. A B C 8m 4m 4m 4m 4m - 50 kN M V 8m 50 kN B C 4m 4m 4m 4m A B C 8m 4m 4m 4m 4m 50 kN + Structural Analysis I Moment Influence Line Exercise Problem Solutions Dr. Structure P a g e | 5 To determine the maximum positive moment at A, place the load at A where the influence line peaks in the positive region, as shown below. The free-body diagram of the beam can be drawn as shown below. Using the above diagram, the moment at A can be determined as: (5 m)(25 kN) 125 kN.m= To determine the maximum negative moment at A, we placed the load at the left end of the beam where the influence line peaks in the negative direction. A B 10m 5m 5m 5m + - - 50 kN A B 10m 5m 5m 5m 50 kN 25 kN 25 kN A B 10m 5m 5m 5m + - - 50 kN Structural Analysis I Moment Influence Line Exercise Problem Solutions Dr. Structure P a g e | 6 The free-body diagram for the beam is shown below. Hence, the maximum negative moment at A equals: (5 m)(50 kN) 250 kN.m= A B 10m 5m 5m 5m 50 kN 75 kN 50 kN Structural Analysis I Moment Influence Line Exercise Problem Solutions Dr. Structure P a g e | 7 Problem 3: Draw the moment influence line for points A and B. Then calculate the maximum positive and negative moments at each point. The beam is subjected to a moving load of 50 kN. Solution: The influence lines for the bending moments at points A and B are shown below. To determine the maximum negative moment at point A, place the load on the beam where the influence line peaks in the negative region, as shown below.