Question

A simply supported beam AB of span 4 m is carrying a point loads of 5, 2 and 3 kN at 1, 2 and 3 m

respectively from the support A. Calculate the reactions at the supports A and B.​

Answer 1

Given: beam AB is 4 meters long. Point loads $5kN,2kN,3kN$ at a distance of $1m,2m,3m$.

To find: reaction at A and B.

Explanation:

Step by step method:

Step 1 of 2

The total reaction force is:

$R_{A} +R_{B} =5kN+2kN+3kN=10kN$

∑$M_{A} =0\\(-5X1)+(-2X2)+(-3X3)+(R_{B}X4)=\\ -5-4-9=-4R_{B}\\R_{B}=\frac{18}{4} \\R_{B}=4.5kN$

Step 2 of 2

$R_{A} +R_{B} =10kN\\R_{A} +4.5 =10kN\\R_{A}=5.5kN$

Final answer

$R_{A}=5.5kN$ and  $R_{B}=4.5kN$