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

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

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

- Asked in: 2074 Chaitra, 16 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-30kn-20knm
- 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 given frame. Indicate numerical values at salient points. [Figure: left column A-B of 5 m (2.5 m + 2.5 m) with A hinged at the base and a 50 kN horizontal force at the mid-height; top member B-C-D with a 30 kN force at $30^\circ$ at B, a 20 kN/m UDL over B to C (4 m), an internal hinge at C, then a triangular load increasing from zero at C to 15 kN/m at D over 9 m; D is a hinged support.]

## Short answer

Support reactions: H_A=25.0 kN right, V_A=117.5 kN up, H_D=101.0 kN left, V_D=45.0 kN up. Diagrams show max bending moment 250.0 kN·m at B (tension left face of AB); local peak 77.94 kN·m (bottom) at 5.20 m from C on CD where shear zero; zero at hinge C.

## Answer

**Assumptions (taken from the figure):**
- A(0,0) hinged; AB = 5 m; 50 kN horizontal (→) at mid-height (2.5 m). Top member B–C–D: BC = 4 m, CD = 9 m, hinge at C, D hinged support at beam level.
- 30 kN at B acts at 30° to the horizontal, to the right and downward; 20 kN/m downward on BC; triangular load on CD from 0 at C to 15 kN/m at D (total 67.5 kN).

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
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A
```

#### 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.

- $H_A$ = 25.00 kN →
- $V_A$ = 117.50 kN ↑
- $H_D$ = 100.98 kN ←
- $V_D$ = 45.00 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 | -117.50 | -25.00 | 0.00 |
| AB at B | -117.50 | -75.00 | -250.00 (left face) |
| BC at B | -100.98 | 102.50 | -250.00 (top) |
| BC at C | -100.98 | 22.50 | 0.00 |
| CD at C | -100.98 | 22.50 | 0.00 |
| CD at D | -100.98 | -45.00 | 0.00 |

#### Shape of the diagrams
- AB: V constant (steps at point loads), M linear
- BC: V linear, M parabolic
- CD: V parabolic, M cubic
- 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 = 250.00 kN·m at B (on AB), tension on the left face
- V = 0 at 5.20 m from C along CD: M = 77.94 (bottom) kN·m (local maximum)
- 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. What is the total triangular load on CD (0 to 15 kN/m over 9 m)?
   A. 135 kN
   B. 15 kN
   C. 67.5 kN
   D. 33.75 kN
   Answer: C. Area of triangle = 1/2 x 9 x 15 = 67.5 kN. (Key point: Triangular load resultant)

2. On CD with the triangular load, V and M are:
   A. V linear, M parabolic
   B. V constant, M linear
   C. V cubic, M parabolic
   D. V parabolic, M cubic
   Answer: D. Triangular load makes V parabolic and M one degree higher, cubic. (Key point: Shapes under triangular load)

3. Where is the maximum bending moment of 250 kN·m?
   A. At B on column AB, tension on the left face
   B. At the hinge C
   C. At D, the hinged support
   D. At A, the hinged base
   Answer: A. M at B is -250 kN·m (left face), while M is zero at A, C and D. (Key point: Maximum moment)

4. What does V = 0 at 5.20 m from C along CD indicate?
   A. The bending moment is zero there
   B. A local maximum of bending moment there (77.94 kN·m)
   C. A point of contraflexure
   D. The axial force is zero there
   Answer: B. Since dM/dx = V, M is stationary where V = 0, giving a local maximum. (Key point: Meaning of V = 0)

## Related in Strength of Materials

- [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 and 20 kN/m, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-30-20) — Strength of Materials, chapter 1
- [Frame AFD, SFD, BMD (100 kN, 25 kN/m, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-100kn-25knm) — Strength of Materials, chapter 1
- [Frame AFD, SFD, BMD (20 kNm, 15 kN)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-20knm-15kn) — Strength of Materials, chapter 1
- [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 (50 kN, 15 kN/m)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-50kn-15knm) — Strength of Materials, chapter 1

## Related in other subjects

- [AFD, SFD, BMD of frame with 60 kN/m UDL](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-bmd-60knm-20knm-12kn) — Applied Mechanics, chapter 6
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