- 2076 Asoj · 12 marks
Frame AFD, SFD, BMD (100 kN, inclined member)
Short answer
Support reactions: HA=0, VA=80.47 kN upward, VD=76.09 kN upward. Axial, shear and bending moment diagrams: AB parabolic, BC and CD linear. Maximum bending moment 152.19 kN·m at C on BC, tension on bottom side.
Draw axial force, shear force and bending moment diagram for a given loaded frame. Also write the salient features. [Figure: hinged support at A at the lower left; inclined member A-B rising to B (slope 3 vertical to 4 horizontal; horizontal projection 2 m, rise 2 m shown) and carrying a 20 kN/m distributed load along it; horizontal member B-C-D with a 100 kN point load at C; B to C 2 m, C to D 2 m; D is the right end, supported as drawn.]
Assumptions (taken from the figure):
- A(0,0) hinged; AB inclined, horizontal projection 2 m and rise 2 m, so B = (2, 2); BC = CD = 2 m horizontal.
- 20 kN/m acts vertically downward on the full inclined length AB (2.83 m, total 56.57 kN); 100 kN downward at C.
- D is taken as a roller (vertical reaction only), which makes the frame determinate.
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.
/B--------------C--------------D
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A
Support reactions
Equilibrium of the whole frame gives , and .
- = 0.00 kN ←
- = 80.47 kN ↑
- = 76.09 kN ↑
Check: the three equilibrium equations of the complete frame (and the hinge condition, where present) are satisfied to rounding (residuals below ).
Axial force, shear force and bending moment at the key sections
| Section | N (kN) | V (kN) | M (kN·m) |
|---|---|---|---|
| AB at A | -56.90 | 56.90 | 0.00 |
| AB at B | -16.90 | 16.90 | 104.38 (right face) |
| BC at B | 0.00 | 23.91 | 104.38 (bottom) |
| BC at C | 0.00 | 23.91 | 152.19 (bottom) |
| CD at C | 0.00 | -76.09 | 152.19 (bottom) |
| CD at D | 0.00 | -76.09 | 0.00 |
Shape of the diagrams
- AB: V linear, M parabolic
- BC: V constant (steps at point loads), M linear
- CD: 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 = 152.19 kN·m at C (on BC), tension on the bottom
✓ Answer checked by Claude Opus 5.5 (high effort)
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