What is meant by influence line?
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 influence line diagram and its significance?
Influence Line Diagram It’s a diagram which shows the reactions, Shear force and Bending moment at each and every section or instant at any distance of any span that you want to find out. In short, Influence Line Diagram shows the influence or effect of loads or reaction on the span.
What is the variation of influence line for stress function in a statically determinate structure?
The variation of influence line for stress function in a statically determinate structure is- parabolic.
What are the uses of influence lines in structural analysis?
The most important use of influence line is finding out the location of a load for which certain response will have a maximum value. For example, we may need to find the location of a moving load (say a gantry) on a beam (say a gantry girder) for which we get the maximum bending moment at a certain point.
Why is influence line necessary for analysis?
Influence line represents the variation of either the reaction, shear, moment, or deflection at a specific point in a member, as a concentrated force moves over the member. Influence lines are important for the design of a structure that resists large live loads moving along the spans such as bridges and cranes.
What is qualitative influence line?
Procedure for constructing qualitative influence lines for indeterminate structures is: (1) remove from the structure the restraint corresponding to the response function of interest, (2) apply a unit displacement or rotation to the released structure at the release in the desired response function direction, and (3) …
What is the role of influence line diagram in Muller Breslau principle?
The principle states that the influence lines of an action (force or moment) assumes the scaled form of the deflection displacement. OR, This principle states that “ordinate of ILD for a reactive force is given by ordinate of elastic curve if a unit deflection is applied in the direction of reactive force.”
What is the shape of influence line diagram for the maximum bending moment in respect of a simply supported beam?
triangular
Hence, the shape of influence line diagram for maximum bending moment in a simply supported beam is triangular in shape.
What is quantitative influence line?
The deflected shape due to the unit deformation will be composed of straight lines and can be used to locate the movable loads to cause maximum effect, and to calculate the magnitude of the force. Such an influence diagram is called a quantitative influence line for a determinate structure.
What is an influence line for an indeterminate structure?
Such an influence diagram is called a quantitative influence line for a determinate structure. Applying a deformation to a statically indeterminate beam or frame will cause the structure to bend and can only be used to locate the position of movable loads (like Live load ) to cause maximum response.
What is the response function of an influence line?
Influence Lines Response Function = support reaction, axial force, shear force, or bending moment. 6. Influence Lines INFLUENCE LINE VS SFD/BMD Influence lines represent the effect of a moving load only at a specified point on a member shear and moment diagrams represent the effect of fixed loads at all points along the member. 7.
What is an influence line for a beam?
Such an influence diagram is called a quantitative influence line. Applying a deformation to a statically indeterminate beam or frame will cause the structure to bend and can only be used to locate the movable loads to cause maximum effect.
How are influence lines determined in virtual work?
Qualitative Influence Lines Müller-Breslau Principle The Müller-Breslau principle is a method to determine influence lines. The derivation of the principle comes from the theory of Virtual work.