---
title: "Four loads on 60 m girder: BM at C, absolute"
subject: "Theory of Structures I"
chapter: 5
key: "semester_4/theory_of_structures_i:train-170-215-150-120-60m"
source: https://www.bctengineer.com/q/semester_4/theory_of_structures_i/train-170-215-150-120-60m
site: BCT Engineering
---

# Four loads on 60 m girder: BM at C, absolute

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

- Asked in: 2073 Bhadra, 12 marks
- Video: [Absolute Maximum Shear and Moment Due To Series of Concentrated Loads in a Simply Supported Beam](https://www.youtube.com/watch?v=LKdXQyK1hgk) — Master Civil Engineering
- 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/train-170-215-150-120-60m
- Whole chapter: https://www.bctengineer.com/md/semester_4/theory_of_structures_i/chapter-5

## Question

Determine maximum bending moment at C and absolute maximum bending moment in the girder shown in figure below when four concentrated loads move from left to right. [Figure: loads 170 kN, 215 kN, 150 kN, 120 kN with spacings 3 m, 2 m, 3 m; girder AB of 60 m; C at 20 m from A.]

## Short answer

Maximum bending moment at C is found by placing the 215 kN load at C, yielding 8093.3 kN m. Absolute maximum bending moment is 9121.0 kN m, occurring under the 215 kN load when placed at 29.70 m from A.

## Answer

**Data:** girder $AB$, $L = 60$ m; section $C$ at $a = 20$ m from $A$, $b = 40$ m. Loads from the rear: 170, 215, 150, 120 kN at spacings 3 m, 2 m, 3 m; the train moves left to right (120 kN leads, as drawn). Total $W = 655$ kN.

#### (i) Maximum BM at C
ILD for $M_C$: peak $\dfrac{ab}{L} = \dfrac{20\times 40}{60} = 13.33$ m; ordinate $\dfrac{2x}{3}$ for $x\le 20$ and $\dfrac{20(60-x)}{60}$ for $x\ge 20$.

Place the 215 kN load at $C$. Load on the left of $C$ including it: $170 + 215 = 385$ kN.

$$
\frac{385}{20} = 19.25 > \frac{655}{60} = 10.9 > \frac{170}{20} = 8.5
$$

The condition for maximum is satisfied. Positions from $A$: 170 kN at 17 m, 215 kN at 20 m (at $C$), 150 kN at 22 m, 120 kN at 25 m.

| Load (kN) | Position (m) | Ordinate (m) | P x y (kN m) |
|---|---|---|---|
| 170 | 17 | 11.333 | 1926.7 |
| 215 | 20 | 13.333 | 2866.7 |
| 150 | 22 | 12.667 | 1900.0 |
| 120 | 25 | 11.667 | 1400.0 |

$$
M_{C,max} = 8093.3\ \text{kN m}
$$

#### (ii) Absolute maximum BM
Distance of the resultant behind the 120 kN load: $\bar x = \dfrac{170(8)+215(5)+150(3)}{655} = 4.405$ m. Trying each load with the resultant placed symmetrically about mid-span:

| Load placed near mid-span (kN) | Position of load (m) | M under it (kN m) |
|---|---|---|
| 170 | 28.20 | 8682.8 |
| 215 | 29.70 | 9121.0 |
| 150 | 30.70 | 9010.4 |
| 120 | 32.20 | 8435.4 |

The largest value is under the 215 kN load, at 29.70 m from $A$. Then the loads are at: 170 kN: 26.70 m, 215 kN: 29.70 m, 150 kN: 31.70 m, 120 kN: 34.70 m (all on the girder).

$$
R_A = 324.2\ \text{kN}, \qquad M_{max} = R_A\times 29.70 - (\text{moments of the loads on its left}) = 9121.0\ \text{kN m}
$$

**Answer: (i) $M_C = 8093.3$ kN m; (ii) absolute maximum BM = 9121.0 kN m under the 215 kN load.**

## Check yourself

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

1. For C at 20 m on a 60 m girder, what is the peak ordinate of M_C ILD?
   A. 20 m
   B. 13.33 m
   C. 15 m
   D. 40 m
   Answer: B. ab/L = 20 x 40 / 60 = 13.33 m. (Key point: Peak ordinate)

2. Which load is placed at C and which check confirms it?
   A. 215 kN; 385/20 > 655/60 > 170/20
   B. 170 kN; 170/20 > 655/60
   C. 150 kN; 535/20
   D. 120 kN; 120/20
   Answer: A. 19.25 > 10.9 > 8.5 satisfies the criterion with the 215 kN load at C. (Key point: Load at C)

3. What is the maximum BM at C?
   A. 9121.0 kN m
   B. 8093.3 kN m
   C. 8682.8 kN m
   D. 2866.7 kN m
   Answer: B. 1926.7 + 2866.7 + 1900.0 + 1400.0 = 8093.3 kN m. (Key point: Maximum BM at C)

4. Where is the absolute maximum BM and its value?
   A. Under the 170 kN load, 8682.8 kN m
   B. Under the 215 kN load at 29.70 m from A, 9121.0 kN m
   C. Under the 150 kN load, 9010.4 kN m
   D. Under the 120 kN load, 8435.4 kN m
   Answer: B. With the resultant (4.405 m behind the leading load) symmetric about mid-span, the largest moment is under the 215 kN load: 9121.0 kN m. (Key point: Absolute maximum)

## Close variants set in other exams

- [Four loads on 100 m girder: BM at C, absolute](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Atrain-100-160-180-120-girder-100m) — Theory of Structures I, chapter 5, asked 2×

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