AFD, SFD, BMD for frame with mixed loads

Reading of the figure: A is a hinge at the base (0, 0) and G is a roller at the base (4, 0). The left column rises to C at (0, 6); B is 2 m above A, and D is a cantilever end 2 m to the left of C. Beam C–E–F: C(0, 6), E(2, 6), F(4, 6). The right column FG is 6 m high. Loads: 20 kN downward at D (cantilever tip); a 20 kN·m couple at C (counter-clockwise; the label reads 20 KN/m but is drawn as a curved arrow); 30 kN at B at 30° (down and to the right); 5 kN/m UDL on EF (2 m); a horizontal triangular load on FG, zero at F and 6 kN/m at G, acting to the left. G is a roller (vertical reaction only).

Support reactions

Loads: 30 kN → (25.98 →, 15 ↓) at B; UDL 5 × 2 = 10 kN ↓ at x = 3 m; triangular load = ½ × 6 × 6 = 18 kN ←, at 2 m above G.

ΣM_A = 0 (anticlockwise +):
  +20×2 (cantilever, 20 kN ↓ at x = −2)  = +40
  +20   (couple)                          = +20
  −25.98 × 2 (horizontal part at B)       = −51.96
  −10 × 3                                  = −30
  +18 × 2 (leftward load at 2 m height)   = +36
  +4 G_y
  =>  4 G_y = −14.04,  G_y = −3.51 kN  (acts downwards, ↓ 3.51 kN)
ΣFx = 0:  A_x + 25.98 − 18 = 0   ->  A_x = −7.98 kN  (7.98 kN ←)
ΣFy = 0:  A_y − 20 − 15 − 10 − 3.51 = 0 -> A_y = 48.51 kN ↑

Member forces

• At joint C the moment in the beam (116.04) = column (56.04) + cantilever (40) + couple (20).
• At F the moment in the beam (72.00) equals the moment at the column top (72.00).
• Column FG: with y up from G, V = 6y − 0.5y², M = 3y² − y³/6; check M(6) = 108 − 36 = 72 kN·m.

BMD (kN·m, tension side drawn)
 D --40-- C(116)------E(89)---F(72)
          |                     |
        (56)                    | 72 at F, curving to 0 at G
         |                      |
       15.96 B                  |
         |                      |
         0 A                   0 G

Salient features: the maximum moment is 116.04 kN·m (hogging) at C, just to the right of the cantilever junction; M = 0 at A, D and G (pinned and free ends); the BC column changes the sign of its moment at 0.89 m above B (point of contraflexure); the shear in the beam is 13.51 kN, then falls linearly to 3.51 kN under the UDL; the roller G has a negative reaction (3.51 kN downwards), so the frame must be anchored there, and the right column is in tension.