---
title: "Frame AFD, SFD, BMD (30 and 20 kN/m, hinge)"
subject: "Strength of Materials"
chapter: 1
key: "semester_3/strength_of_materials:frame-afd-sfd-bmd-30-20"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/frame-afd-sfd-bmd-30-20
site: BCT Engineering
---

# Frame AFD, SFD, BMD (30 and 20 kN/m, hinge)

Strength of Materials · Chapter 1: Axial Forces, Shearing Forces and Bending Moments

- Asked in: 2070 Chaitra, 12 marks
- Video: [ANALYSIS OF FRAME SHEAR BENDING & AXIAL THRUST DIAGRAM | EX 03](https://www.youtube.com/watch?v=VhZ1_8AFJrI) — Structural Funda by:- KheNiSiR
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/frame-afd-sfd-bmd-30-20
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-1

## Question

Draw axial force, shear force and bending moment diagram for the frame shown in figure below. [Figure: left column A-B 8 m high with A hinged and a 30 kN horizontal force at B; top member B-C-D with a 30 kN/m triangular load over B to C (6 m), an internal hinge at C, and 20 kN/m UDL over C to D (6 m); inclined member from D down to E, a hinged support 12 m below, 5 m to the right horizontally; horizontal dimensions 6 m, 6 m, 5 m.]

## Short answer

Reactions: Ha=47.25→, Va=93.00↑, He=77.25←, Ve=117.00↑. AB: N=-93, V=-47.25, M linear 0→-378 kN·m left face. BC: triangular load, M cubic to 0 at hinge C. CD: UDL, M parabolic from 0 to -342 top at D. DE: N=-137.71, V=26.31, M linear -342→0. Max BM=378 kN·m at B.

## Answer

**Assumptions (taken from the figure):**
- A(0,0) hinged; AB = 8 m; 30 kN horizontal (→) at B. Beam B–C–D: BC = CD = 6 m; hinge at C.
- Triangular load on BC from 0 at B to 30 kN/m at C; 20 kN/m on CD (both downward).
- Inclined member DE: horizontal 5 m, vertical 12 m downward, so E = (17, −4) is the hinged support (length 13 m).

Sign convention: N is positive in tension; V is positive when the forces on the part before the section (travelling A → end) point along the left-hand normal of the member axis (upward on a left-to-right beam); M is quoted as a magnitude with the tension face named. Support reactions are drawn on the free-body of the whole frame.

```text
B------------C------------D
|                          \
|                          \\
|                            \
|                            \\
|                             \
|                              \\
|                               \
|                               \\
A                                 \
                                  \\
                                   \
                                    \\
                                     E
```

#### Support reactions
Equilibrium of the whole frame gives $\Sigma F_x = 0$, $\Sigma F_y = 0$ and $\Sigma M = 0$; the internal hinge adds the condition $M_{hinge} = 0$ (moments of all forces on one side of the hinge), which makes the reactions determinate.

- $H_A$ = 47.25 kN →
- $V_A$ = 93.00 kN ↑
- $H_E$ = 77.25 kN ←
- $V_E$ = 117.00 kN ↑

Check: the three equilibrium equations of the complete frame (and the hinge condition, where present) are satisfied to rounding (residuals below $10^{-9}$).

#### Axial force, shear force and bending moment at the key sections
| Section | N (kN) | V (kN) | M (kN·m) |
|---|---|---|---|
| AB at A | -93.00 | -47.25 | 0.00 |
| AB at B | -93.00 | -47.25 | -378.00 (left face) |
| BC at B | -77.25 | 93.00 | -378.00 (top) |
| BC at C | -77.25 | 3.00 | 0.00 |
| CD at C | -77.25 | 3.00 | 0.00 |
| CD at D | -77.25 | -117.00 | -342.00 (top) |
| DE at D | -137.71 | 26.31 | -342.00 (right face) |
| DE at E | -137.71 | 26.31 | 0.00 |

#### Shape of the diagrams
- AB: V constant (steps at point loads), M linear
- BC: V parabolic, M cubic
- CD: V linear, M parabolic
- DE: V constant (steps at point loads), M linear
- AFD: constant between loads on a member, changing only where a load component acts along the member.
- BMD is drawn on the tension side of each member; it is continuous at rigid joints (moment is transferred) and zero at hinges and at free ends.

#### Salient features
- Maximum bending moment = 378.00 kN·m at B (on AB), tension on the left face
- V = 0 at 0.15 m from C along CD: M = 0.23 (bottom) kN·m (local maximum)
- Point of contraflexure (M = 0) at 0.30 m from C along CD
- Bending moment is zero at the internal hinge (value read from both sides: 0.00).

## Check yourself

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

1. On BC with triangular load and a hinge at C, which is true?
   A. V linear, M parabolic, M maximum at C
   B. V parabolic, M cubic, and M = 0 at C
   C. V constant, M linear, M = 0 at B
   D. V parabolic, M non-zero at C
   Answer: B. Triangular load gives parabolic V and cubic M, and the hinge forces M = 0. (Key point: Hinge and shapes)

2. Maximum bending moment is:
   A. 342 kN·m at D
   B. 378 kN·m at C
   C. 378 kN·m at B, tension on left face of AB
   D. 0.23 kN·m on CD
   Answer: C. M_B = -378 kN·m is the largest; M_D = -342. (Key point: Maximum moment)

3. Point of contraflexure at 0.30 m from C on CD means:
   A. V changes sign
   B. N is zero
   C. Deflection is maximum
   D. M changes sign there
   Answer: D. Contraflexure is where bending moment passes through zero and changes sign. (Key point: Contraflexure)

## Related in Strength of Materials

- [Frame AFD, SFD, BMD (80 kN, 30 kNm, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-80kn-30knm) — Strength of Materials, chapter 1
- [Frame AFD, SFD, BMD (30 kN/m, 50 kNm, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-30knm-50knm) — Strength of Materials, chapter 1
- [Frame AFD, SFD, BMD (30 kN, 20 kN/m)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-30kn-20knm) — Strength of Materials, chapter 1
- [Frame AFD, SFD, BMD (inclined column, triangular)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-30knm-20kn) — Strength of Materials, chapter 1
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## Related in other subjects

- [AFD, SFD, BMD of frame with triangular load](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-bmd-30knm-10knm-triangular-hinge) — Applied Mechanics, chapter 6, asked 2×
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