Frame AFD, SFD, BMD (20 kNm, 15 kN)

Assumptions (taken from the figure):

• A(0,0) hinged; AB = 6 m; beam B–C = 4 m; column C–G = 6 m with G hinged; overhang C–E = 2 m carrying 15 kN downward at E.
• Load on AB: horizontal, varying from 10 kN/m at A to 5 kN/m at B (acting →); 5 kN/m downward on BC; 20 kN·m couple at C (clockwise); 10 kN at 30° to the horizontal acts at mid-height of CG, to the right and downward.
• Two hinged supports with no internal hinge are indeterminate, so a hinge is assumed at the mid-span of BC.

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
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A                G

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.

• $H_A$ = 39.67 kN ←
• $V_A$ = 39.00 kN ↓
• $H_G$ = 14.00 kN ←
• $V_G$ = 79.00 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

Shape of the diagrams

• AB: V parabolic, M cubic
• BC: V linear, M parabolic
• CG: 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 = 107.99 kN·m at C (on BC), tension on the top
• V = 0 at 5.01 m from A along AB: M = 90.69 (right face) kN·m (local maximum)
• Point of contraflexure (M = 0) at 2.00 m from B along BC
• Bending moment is zero at the internal hinge (value read from both sides: 0.00).