Question 2 of 3 · Trusses & Structural Analysis · Advanced · About 35 min

Braced rectangular lifting frame

A pin-jointed truss has joints $A=(0,0)$ , $B=(3,0)$ , $C=(3,2)$ and $D=(0,2)$ metres, and members $AB,BC,CD,DA,AC$ . $A$ is pinned and $B$ is a vertical roller. At joint $C$ , a $6\,\mathrm{kN}$ downward force and a $4\,\mathrm{kN}$ force to the right act simultaneously. Determine all support reactions and member forces; use positive axial force for tension.

A pin-jointed rectangular truss with joints A (0, 0), B (3, 0), C (3, 2) and D (0, 2) in metres. Exactly five members: AB, BC, CD, DA and the single diagonal AC. There is no member BD. A on a pin support, B on a roller support. At joint C, two separate force arrows: one above the joint pointing down into it, and one to the right pointing away from it. Keep the two force labels well apart. Dimensions of 3.0 m under the base and 2.0 m beside member DA. Labels: A; B; C; D; 6 kN on the downward arrow; 4 kN on the rightward arrow; 3.0 m; 2.0 m — Schematic, not to scale unless dimensions are given.

Given

Rectangular 3 m by 2 m
Pin A, roller B
At C: $F_x=+4$ kN, $F_y=-6$ kN

Find

$A_x,A_y,B_y$

Assumptions

All members and connections are idealised as specified in the question.
Use g = 9.81 m/s^2 where gravitational acceleration is required.

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Braced rectangular lifting frame

Given

Find

Assumptions

Worked solution