Question
Download Solution PDFA single rolling load of 40 kN rolls from left end along a simply supported girder of span 20 m. The absolute maximum positive and negative shear force, respectively are:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Influence line diagram:
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. ILD can be drawn for statically determinate as well as indeterminate structures.
Advantages of drawing ILD are as follows:
i) To determine the value of a quantity (shear force, bending moment, deflection, etc.) for a given system of loads on the span of the structure.
ii) To determine the position of a live load for the quantity to have the maximum value and hence to compute the maximum value of the quantity.
Explanation:
Rolling load = 40 kN
Maximum positive shear force:
When rolling load will be acting at point A then the shear force will be maximum.
Maximum shear force = Magnitude of load × ordinate of ILD under the load
= 40 × 1 = 40 kN (+)
Maximum negative shear force:
When rolling load will be acting at point B then the shear force will be maximum.
Maximum shear force = Magnitude of load × ordinate of ILD under the load
= 40 × 1 = 40 kN (-).
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