A beam is loaded with a uniformly distributed load between the two roller supports and a single load at the overhang. It also has two internal hinges - one midway between the fixed support and the first roller support and the other midway between the two roller supports. Refer to the figure below for the magnitude of the loadings and dimensions. a) Draw the FBD of the beam and determine if the beam is statically determinate or indeterminate. 75 kN/m 100 KN 12.5 m 12.5 m 7.5 m 7.5 m 10 m b) If the beam is statically determinate, analyse it using the equilibrium equations. If the beam is statically indeterminate, analyse it using structural indeterminate methodologies such as setting up and solving the equations of equilibrium, equations of compatibility, and force-displacement relations. 1. Draw the FBD for each element of the beam and determine the axial forces, shear forces, and bending moments for each element. 2. Once all forces and moments are calculated, draw the FBD of the whole beam with the calculated forces and moments. 3. Draw the shear force diagram for the beam. Ensure that you show all your calculations for the diagram, including the location of zero shear (uniformly distributed load). 4. Draw the bending moment diagram for the beam. Ensure that you show all your calculations for the diagram.
A beam is loaded with a uniformly distributed load between the two roller supports and a single load at the overhang. It also has two internal hinges - one midway between the fixed support and the first roller support and the other midway between the two roller supports. Refer to the figure below for the magnitude of the loadings and dimensions. a) Draw the FBD of the beam and determine if the beam is statically determinate or indeterminate. 75 kN/m 100 KN 12.5 m 12.5 m 7.5 m 7.5 m 10 m b) If the beam is statically determinate, analyse it using the equilibrium equations. If the beam is statically indeterminate, analyse it using structural indeterminate methodologies such as setting up and solving the equations of equilibrium, equations of compatibility, and force-displacement relations. 1. Draw the FBD for each element of the beam and determine the axial forces, shear forces, and bending moments for each element. 2. Once all forces and moments are calculated, draw the FBD of the whole beam with the calculated forces and moments. 3. Draw the shear force diagram for the beam. Ensure that you show all your calculations for the diagram, including the location of zero shear (uniformly distributed load). 4. Draw the bending moment diagram for the beam. Ensure that you show all your calculations for the diagram.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A beam is loaded with a uniformly distributed load between the two roller supports and a single load at the overhang.
It also has two internal hinges - one midway between the fixed support and the first roller support and the other
midway between the two roller supports. Refer to the figure below for the magnitude of the loadings and dimensions.
a) Draw the FBD of the beam and determine if the beam is statically determinate or indeterminate.
75 kN/m
100 KN
12.5 m
12.5 m
7.5 m 7.5 m
10 m
b) If the beam is statically determinate, analyse it using the equilibrium equations. If the beam is statically
indeterminate, analyse it using structural indeterminate methodologies such as setting up and solving the equations
of equilibrium, equations of compatibility, and force-displacement relations.
1. Draw the FBD for each element of the beam and determine the axial forces, shear forces, and bending
moments for each element.
2. Once all forces and moments are calculated, draw the FBD of the whole beam with the calculated forces and
moments.
3. Draw the shear force diagram for the beam. Ensure that you show all your calculations for the diagram,
including the location of zero shear (uniformly distributed load).
4. Draw the bending moment diagram for the beam. Ensure that you show all your calculations for the diagram.
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