Question 1 of 3 · Trusses & Structural Analysis · Intermediate · About 22 min

Roof-frame king-post truss

A symmetric king-post roof truss has joints $A=(0,0)$ , $B=(3,2.25)$ , $C=(6,0)$ , and $D=(3,0)$ in metres. Bars $AB$ , $BC$ , $AD$ , $DC$ and $BD$ are pin connected. A vertical $18\,\mathrm{kN}$ load acts downward at $B$ ; $A$ is pinned and $C$ is on a roller. Determine the axial force in every bar, specifying tension, compression or zero force.

A symmetric king-post roof truss with joints A (0, 0), D (3, 0), C (6, 0) and B (3, 2.25) in metres. Exactly five members: AB, BC, AD, DC and BD. A on a pin support, C on a roller support. A downward force arrow above B, pointing into the joint. Dimensions of 3.0 m and 3.0 m under the bottom chord, and 2.25 m beside member BD. Labels: A; B; C; D; 18 kN; 3.0 m; 3.0 m; 2.25 m — Schematic, not to scale unless dimensions are given.

Given

$AB=BC=3.75$ m
$P=18$ kN down at B
Five straight two-force members

Find

Support reactions
Forces in $AB,BC,AD,DC,BD$ and nature

Assumptions

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

Independent Waypoint Mentor learning material. Not affiliated with or endorsed by any university.

Roof-frame king-post truss

Given

Find

Assumptions

Worked solution