---
title: "Define influence line diagram and its uses"
subject: "Theory of Structures I"
chapter: 5
key: "semester_4/theory_of_structures_i:define-ild-uses"
source: https://www.bctengineer.com/q/semester_4/theory_of_structures_i/define-ild-uses
site: BCT Engineering
---

# Define influence line diagram and its uses

Theory of Structures I · Chapter 5: Influence Lines for Simple Structures

- Asked in: 2081 Chaitra, 4 marks; 2079 Chaitra, 2 marks; 2074 Bhadra, 4 marks; 2072 Magh, 4 marks; 2069 Bhadra, 2+2 marks (asked 5 times)
- Video: [Influence Lines - Structural Analysis](https://www.youtube.com/watch?v=mdE6Box5lFM) — structurefree
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/theory_of_structures_i/define-ild-uses
- Whole chapter: https://www.bctengineer.com/md/semester_4/theory_of_structures_i/chapter-5

## Question

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.

## 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.

## Answer

#### 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
1. **Critical load position:** it shows where to place live loads (trucks, train wheels, UDL) to produce the maximum value of a quantity.
2. **Maximum values:** for concentrated loads $F = \sum P\,y$; for UDL $F = w\times\text{area}$. This gives the design reaction, shear, moment or member force.
3. **Design of bridges, girders and crane girders:** moving loads decide the sections of bridge girders, trusses, floor beams and gantry girders.
4. **Truss design:** ILDs for chord, web and counter members show whether a member changes sign (stress reversal) and how much counter bracing is needed.
5. **Absolute maximum BM and SF** under a train of wheel loads can be found quickly.
6. **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 |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does an influence line diagram show?
   A. How a quantity at one fixed location varies as a unit load moves across the structure
   B. The value of a quantity at every section for fixed loads
   C. The deflected shape under dead load
   D. The total load on the structure
   Answer: A. An ILD plots the effect at one fixed section against the position of a moving unit load. (Key point: Definition)

2. What is the main use of an ILD in bridge design?
   A. To find the load position giving the maximum value of a quantity
   B. To find the self weight of the girder
   C. To find the material strength
   D. To draw the BMD for dead loads
   Answer: A. ILDs locate the critical position of live loads and give the maximum design reaction, shear or moment. (Key point: Use)

3. Which statement correctly contrasts an ILD with a BMD?
   A. ILD: section fixed, load position variable; BMD: load fixed, section variable
   B. ILD: load fixed, section variable; BMD: section fixed, load variable
   C. Both have the same units
   D. ILD needs actual loads and BMD uses a unit load
   Answer: A. The ILD ordinate is the effect at one section against load position, while the BMD gives the effect along sections for fixed loads. (Key point: Difference from BMD)

4. What are the units of a bending moment ILD ordinate?
   A. Length (m), as moment per unit load
   B. kN m
   C. kN
   D. Dimensionless
   Answer: A. A unit load gives moment in units of (kN m)/kN = m. (Key point: Units)

## Related in Theory of Structures I

- [Overhang beam ILD for shear force at C](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Aoverhang-ild-sf-c-2071o) — Theory of Structures I, chapter 5
- [Cantilever strain energy: bending, shear, torsion](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Acantilever-strain-energy-circular-4m) — Theory of Structures I, chapter 2, asked 2×
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- [Arch: reactions, BM, thrust and shear at D by ILD](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Aarch-50m-udl-50kn-ild-d-15m) — Theory of Structures I, chapter 6
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- [No bending moment under UDL in parabolic arch](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Aarch-no-bm-udl) — Theory of Structures I, chapter 6, asked 2×

## Related in other subjects

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