A cantilever beam is loaded as shown below with a uniform lo

A cantilever beam is loaded as shown below, with a uniform load, w, over the first L1= 4.8 m, and a linearly decreasing load/unit length over the final L2= 4.3 m. Calculate the centroidal position of the applied load.

Solution

>> Let\'s consider all the forces individually :

1). F1, force due to uniform loading , w , over first L1 = 4.8 m

=> F1 = 4.8*w ..........(1).......

>> Now, the load is decreasing linearly from w to 0, over L2 = 4.3 m

2). So, F2 ,Force in this area = (1/2)w*L2

and it acts at a distance of L1 + L2/3 from left end side

>> Now, Let Net Force, F = F1 + F2 is acting at a distance \"x\"

>> So, balancing moments,

=> F*x = F1*L1/2 + F2*(L1 + L2/3)

=> (4.8*w + 0.5*w*4.3)*x = 4.8*w*2.4 + (1/2)w*4.3*(4.8+4.3/3)

=> Solving, x = 3.59 m ........ANSWER.........