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Define influence line diagram and its uses
Short answer
An influence line diagram shows variation of a structural quantity at a fixed point as a unit load moves. It determines critical live-load positions, maximum design values, and differs from BMD/SFD which show distribution over the span for fixed loads.
Define influence line diagram. Explain its uses (in design of bridges and girders, and in Civil Engineering) and how it differs from other structural quantity diagrams like bending moment diagram and shear force diagram.
Definition
An influence line diagram (ILD) is a graph that shows how a particular structural quantity (reaction, shear force, bending moment, axial force in a member, or deflection) at one fixed location varies as a unit load moves across the structure. The ordinate at any point gives the value of that quantity at the fixed location when the unit load is at that point.
Uses
- Critical load position: it shows where to place live loads (trucks, train wheels, UDL) to produce the maximum value of a quantity.
- Maximum values: for concentrated loads ; for UDL . This gives the design reaction, shear, moment or member force.
- Design of bridges, girders and crane girders: moving loads decide the sections of bridge girders, trusses, floor beams and gantry girders.
- Truss design: ILDs for chord, web and counter members show whether a member changes sign (stress reversal) and how much counter bracing is needed.
- Absolute maximum BM and SF under a train of wheel loads can be found quickly.
- Used in Civil Engineering: bridge and highway loading (IRC/AASHTO truck, IRC class loads), railway bridges, overhead cranes, and as the basis of Müller-Breslau's principle for indeterminate structures.
Difference from BMD / SFD
| Influence line diagram | BMD / SFD |
|---|---|
| Shows the effect at one fixed section for a load moving over the structure | Shows the effect at all sections for loads fixed in position |
| Ordinate: value of quantity at the section when unit load is at that point | Ordinate: value at that section due to the fixed loads |
| Load position is the variable | Section position is the variable |
| Needs a unit load, no load values | Needs the actual loads |
| Used for moving/live loads | Used for fixed/dead loads |
| Has units of the quantity per unit load (e.g. m for BM) | Has units of force or moment |
| Positive and negative ordinates show sign changes with load position | Shows sign along the span |
✓ Answer checked by Claude Opus 5.5 (high effort)
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