Question

A uniform beam weighing 1800 N is supported at E and F by cable ABCD. Determine the tension (in N) in segment AB of this cable (correct to 1-decimal place). Assume the cable ABCD, BE and CF to be weightless______

• A. 1311.96

Answer 1

The correct option is A 1311.96
Taking Moment about A,

$R_D\times 4=1800\times 1.5$
$\Rightarrow R_D=675N$
$\therefore R_A=1800-R_D=1125N$
At joint D,

$T_{CD}=\frac{R_D}{sin45}=675\sqrt{2}N$

Taking free body diagram as shown in figure


$T_{AB}sin\theta +675\sqrt{2}sin{45}^{\circ }=1800$
$T_{AB}sin\theta =1125\text{....(i)}$

$\sum H=0$
$T_{AB}cos\theta =675\sqrt{2}cos{45}^{\circ }$
$\Rightarrow$ $T_{AB}cos\theta =675\text{....(ii)}$

From equation (i) & (ii)
$\tan \theta =\frac{5}{3}$

$\Rightarrow \sin \theta =0.8575$

$\text{putting value of}\sin \theta \text{in equation (i)}$

$T_{AB}\times 0.8575=1125$
$T_{AB}=1311.96N$
$T_{AB}=1311.96N$