Question

a truss of a span 7.5m is loaded as shown in figure. find the reaction and forces in the members of the truss​

Answer 1

Answer:

Let, $V_A$ and $V_B$ be the reactions at supports A and B.

Taking moment about A, $\sum$M$_A$ = 0

V$_B$ (7.5) = 5 kN

V$_B$ = 0.67 kN

V$_A$ + V$_B$ = 1 kN,

V$_A$ = 0.33 kN

Consider Joint A:

$\sum$V = 0, Resolving forces vertically

F$_{AC}$ sin 30° = V$_A$ = 0.33

F$_{AC}$ = 0.33/sin 30° = 0.67 kN

$\sum$H = 0, Resolving forces horizontally

F$_{AC}$ cos 30° = F$_{AD}$

F$_{AD}$ = 0.67 × cos 30° = 0.58 kN (Tension)

Consider Joint B:

$\sum$V = 0, Resolving forces vertically

F$_{BC}$ sin 30° = V$_B$ = 0.67 kN

F$_{BC}$ = 0.67/sin 30° = 1.33 kN

$\sum$H = 0, Resolving forces horizontally

F$_{BC}$ cos 30° = F$_{BD}$

F$_{BD}$ = 1.33 × cos 30° = 1.16 kN (Tension)

Consider Joint D:

$\sum$V = 0, Resolving vertically

F$_{DC}$ sin 60° = 1 kN

F$_{DC}$ = 1/sin 60° = 1.16 kN (Tension)

Check:

$\sum$H = 0, Resolving horizontally

F$_{DC}$ cos 30° + 0.58 = F$_{DB}$ = 1.16

F$_{DC}$ = (1.16 - 0.58)/ cos 30° = 1.16 kN (Checked)

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