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How do you calculate influence lines?

How do you calculate influence lines?

Influence line for Reaction at a support

  1. RB = x/L (straight line equation)
  2. RA = 1- x/L (straight line equation)
  3. FC = -RB = – x/L ;when load is between A and C.
  4. FC = RA = 1- x/L ;when the load is between C and B.
  5. MC = RB . (L-a) ; when unit load is between A and C.
  6. MC = RA . (a) ; when unit load is between C and B.

What is determinate truss?

A truss is considered statically determinate if all of its support reactions and member forces can be calculated using only the equations of static equilibrium. For a planar truss to be statically determinate, the number of members plus the number of support reactions must not exceed the number of joints times 2.

What is influence line in structural analysis?

An influence line for a given function, such as a reaction, axial force, shear force, or bending moment, is a graph that shows the variation of that function at any given point on a structure due to the application of a unit load at any point on the structure.

What is a determinate structure?

[də′tər·mə·nət ′strək·chər] (mechanics) A structure in which the equations of statics alone are sufficient to determine the stresses and reactions.

What is the importance of using indeterminate structures?

Indeterminate structures have more members and/or support reactions than required for static stability, so if a part (or member or support) of such a structure fails, the entire structure will not necessarily collapse, and the loads will be redistributed to the adjacent portions of the structure.

What is the difference between an influence line and a truss?

Another important difference for influence lines for trusses is that we must assume that the load can only be transferred to the truss at the intersection points between the members. This is necessary because the truss members themselves are often assumed in design to only take axial forces.

How do you find the reaction influence lines for trusses?

To find those member influence lines, we first have to find the influence lines for the reactions at A and D (IL A y and IL D y ). Since we can use external equilibrium to find the reactions, the process of finding reaction influence lines for trusses is the same as it was for beams.

What is an example of a truss bridge?

An example truss for a road bridge is shown in Figure 6.11. On this truss, the road surface is level with the lower chord of the truss. Therefore, an influence line for this truss would be constructed along a direct line that joins the pin at the left with the roller on the right along the lower chord of the truss.

How do you convert indeterminate to determinate?

Force (Flexibility) Method Convert the indeterminate structure to a determinate one by removing some unknown forces / support reactions and replacing them with (assumed) known / unit forces. Using superposition, calculate the force that would be required to achieve compatibilitywith the original structure.