An arch bridge consists of a circular arch and a horizontal beam, which are hinged together...

Transcribed Image Text:

An arch bridge consists of a circular arch and a horizontal beam, which are hinged together according to the attached picture. The width of the beam is b and the height is h. The circular arc heats up by AT. No other loads occur. How big is the force F on the beam? It is assumed that the bending stiffness Elk of the arch is much larger than the beam El, and that the compression stiffness EAk of the arch is very large. a) Draw a picture of the bending of the structure. (1 p.) b) Solve the symbolic expression for the force F. (2 p.) c) Calculate the numerical value of the point force F when b = 0.5 m, h = 1.5 m, L = 10 m, r = 5 m, E = 36000000 kN/m, coefficient of thermal expansion = 1/10000 1/C and AT = 50 C. (2 p.) Instructions: Use beam bending tables. L/2 L/2 * * Elk >> Elp r EAK 00 =8 AT r h b An arch bridge consists of a circular arch and a horizontal beam, which are hinged together according to the attached picture. The width of the beam is b and the height is h. The circular arc heats up by AT. No other loads occur. How big is the force F on the beam? It is assumed that the bending stiffness Elk of the arch is much larger than the beam El, and that the compression stiffness EAk of the arch is very large. a) Draw a picture of the bending of the structure. (1 p.) b) Solve the symbolic expression for the force F. (2 p.) c) Calculate the numerical value of the point force F when b = 0.5 m, h = 1.5 m, L = 10 m, r = 5 m, E = 36000000 kN/m, coefficient of thermal expansion = 1/10000 1/C and AT = 50 C. (2 p.) Instructions: Use beam bending tables. L/2 L/2 * * Elk >> Elp r EAK 00 =8 AT r h b