Influence line diagram graphically demonstrates how would the resultant force in beam change with respect to the position of load. This diagram is very useful to aid the designer in designing structure that carries moving load, such as bridge.
The procedure to construct the influence line diagram is the same for all statically determinate beam. First, a unit load is loaded on beam to define the function of internal forces or reactions we interested in. Then, the diagram is produced by calculating the value of forces for different load position, and join the plotted points in a diagram.
The use of influence line diagram varies with the type of loading. If there is a concentrated load, the actual force developed in beam is the product of that load value and the value obtained from influence line diagram at that location. On the other hand, forces due to uniformly distributed load should be determined by taking the product of load value and area under the diagram.
The following shows the procedure to produce and use influence line diagram. Watch the video above for full details.
Beam overview
Beam with length L and a unit load located at x from support A.
Support reaction
Determine expression for By using moment equilibrium about A.
Support reaction
Determine expression for Ay using equilibrium along y.
Support reaction influence line diagram
Determine the value of reaction for various x, and plot diagram.
Point C
Point C is defined to determine the influence line diagram of its internal forces.
Internal force functions
For case 1 where the unit load located between point A and C.
Internal force functions
For case 2 where the unit load located beyond point A and C.
Development of influence line diagram
For the case where a=0.1L.
Development of influence line diagram
For the case where a=0.2L.
Development of influence line diagram
For the case where a=0.3L.
Development of influence line diagram
For the case where a=0.4L.
Development of influence line diagram
For the case where a=0.5L.
Application of influence line diagram
For concentrated load, multiply the load value with the value obtained from diagram at the loaded point to calculate the actual force developed.
Application of influence line diagram
For uniformly distributed load, multiply the load value with the area under diagram at loaded portion to calculate the actual force developed.
Application of influence line diagram
For series of concentrated load, use trial and error by placing the first load of the series and coincide with the peak of diagrams.
Application of influence line diagram
Use trial and error by placing the second load of the series and coincide with the peak of diagrams.
Application of influence line diagram
Use trial and error by placing the third load of the series and coincide with the peak of diagrams.
Application of influence line diagram
To determine the maximum bending moment in a simply supported beam, solution without trial and error is possible.
0 Comments