--- title: "Frame AFD, SFD, BMD (5 kN/m, 10 kN, hinge)" subject: "Strength of Materials" chapter: 1 key: "semester_3/strength_of_materials:frame-afd-sfd-bmd-5knm-10kn" source: https://www.bctengineer.com/q/semester_3/strength_of_materials/frame-afd-sfd-bmd-5knm-10kn site: BCT Engineering --- # Frame AFD, SFD, BMD (5 kN/m, 10 kN, hinge) Strength of Materials · Chapter 1: Axial Forces, Shearing Forces and Bending Moments - Asked in: 2074 Asoj, 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-5knm-10kn - Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-1 ## Question Draw axial force, shear force and bending moment diagrams for the frame shown in figure below, indicating the principal numerical values at salient points. [Figure: left column A-B with A hinged at the base, carrying a triangular horizontal load from 10 kN/m at A to 2 kN/m at B; horizontal member B-C-D-E with a 5 kN/m UDL over B to D, an internal hinge at C, a 10 kN downward point load at E; right column D-F with F hinged at the base; horizontal dimensions 3 m, 3 m, 2 m; vertical dimensions 2 m, 3 m, 1 m on the right.] ## Short answer By equilibrium with hinge at C, reactions are found (H_A=21.67 kN left, V_A=1.94 kN up, H_F=8.33 kN left, V_F=38.06 kN up). Diagrams show max bending moment 61.67 kN·m at D on CD (tension top); zero at hinge C; local maxima 27.32 kN·m on AB and 17.04 kN·m on BC where shear vanishes. Overhang DE has linear moment to 20 kN·m hogging at D. ## Answer **Assumptions (taken from the figure):** - A(0,0) hinged; AB = 5 m; horizontal triangular load from 10 kN/m at A to 2 kN/m at B (→). Beam B–C–D–E: BC = CD = 3 m, DE = 2 m; hinge at C. - 5 kN/m downward over B to D; 10 kN downward at E (overhang). Right column DF = 5 m, F hinged at ground level. - The overhang DE is replaced at D by 10 kN downward plus a hogging moment $10\times2 = 20$ kN·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 F ``` #### 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. - $H_A$ = 21.67 kN ← - $V_A$ = 1.94 kN ↑ - $H_F$ = 8.33 kN ← - $V_F$ = 38.06 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 | -1.94 | 21.67 | 0.00 | | AB at B | -1.94 | -8.33 | 16.67 (right face) | | BC at B | -8.33 | 1.94 | 16.67 (bottom) | | BC at C | -8.33 | -13.06 | 0.00 | | CD at C | -8.33 | -13.06 | 0.00 | | CD at D | -8.33 | -28.06 | -61.67 (top) | | DF at D | -38.06 | 8.33 | -41.67 (right face) | | DF at F | -38.06 | 8.33 | 0.00 | #### Shape of the diagrams - AB: V parabolic, M cubic - BC: V linear, M parabolic - CD: V linear, M parabolic - DF: 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 = 61.67 kN·m at D (on CD), tension on the top - V = 0 at 2.79 m from A along AB: M = 27.32 (right face) kN·m (local maximum) - V = 0 at 0.39 m from B along BC: M = 17.04 (bottom) kN·m (local maximum) - Bending moment is zero at the internal hinge (value read from both sides: 0.00). - Overhang DE: V = 10 kN (constant), M = 0 at E varying linearly to 20 kN·m (hogging, tension on top) at D. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the overhang DE with 10 kN at E treated at D? A. Replaced by 10 kN only B. Replaced by a 20 kN horizontal force C. Ignored since it is outside the supports D. Replaced by 10 kN down plus a 20 kN·m hogging moment at D Answer: D. Moving the load to D adds a moment 10 x 2 = 20 kN·m (tension on top), and the overhang has V = 10 kN, M varying 0 to 20. (Key point: Overhang replacement) 2. The column AB carries a triangular horizontal load. The V and M diagrams are: A. V parabolic, M cubic B. V linear, M parabolic C. V constant, M linear D. V cubic, M parabolic Answer: A. A triangular (linearly varying) load gives parabolic shear and cubic moment. (Key point: Shapes on AB) 3. The maximum bending moment is: A. 16.67 kN·m at B B. 61.67 kN·m at D, tension on top C. 27.32 kN·m on AB D. 17.04 kN·m on BC Answer: B. Local maxima are 27.32 and 17.04 kN·m but the joint moment at D (61.67) is greatest. (Key point: Maximum moment) 4. With no load on the column DF, what are V and M? A. V linear, M parabolic B. V zero, M constant C. V constant, M linear from 41.67 at D to 0 at F D. V parabolic, M cubic Answer: C. With no load along the member, V is constant (8.33 kN) and M is linear, falling to zero at the hinge F. (Key point: Column DF) ## Close variants set in other exams - [Frame AFD, SFD, BMD (5 and 10 kN/m, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-5knm-10knm) — Strength of Materials, chapter 1, asked 2× ## Related in Strength of Materials - [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 (10 kN/m, 60 kN, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-10knm-60kn) — 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 (5 and 10 kN/m)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-5knm-2) — Strength of Materials, chapter 1 - [Frame AFD, SFD, BMD (12 kN, 25 kNm, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-12kn-25knm) — 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 ## Related in other subjects - [AFD, SFD, BMD of frame with hinge at D](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-bmd-8knm-hinge-50kn) — Applied Mechanics, chapter 6 - [AFD, SFD, BMD of frame with hinge](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-bmd-hinge-4knm-20knm) — Applied Mechanics, chapter 6 - [AFD, SFD, BMD for frame with internal hinge](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-internal-hinge-5kn-per-m) — Applied Mechanics, chapter 6 - [AFD, SFD, BMD of frame with hinge at C](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-bmd-hinge-5knm-10knm-triangular) — Applied Mechanics, chapter 6, asked 2×