Extreme Beam
Can someone please calculate the reactions for my simply supported beam?
beam 8m long. u.d.l across full length with a force of 2kN. A 30kN point load 2m in from the left have side. Calculate R1 & R2 ( both at extreme edges of beam. 0,0 & 8,0)
I will recycle a picture I used before
http://img44.imageshack.us/img44/9434/iea.gif
Because of the symmetry of the uniformly distributed load, we can place it at the center location L/2. w is the load per unit length, wL is the total load
Moments about R1: (CCW defined as positive)
Moment due to R2: R2*L
Moment due to the UDL: -wL*L/2
Moment due to the point load W: -W*a
Moment due to R1: zero, because it is applied at the reference point
Add up and equate to zero:
R2*L – wL*L/2 – W*a = 0
solve for R2:
R2 = wL/2 + W*a/L
Balance forces:
R1 + R2 = wL + W
R1 = wL + W – R2
R1 = wL + W – wL/2 – W*a/L
Simplify:
R1 = wL/2 + W*(1 – a/L)
Summary:
R1 = wL/2 + W*(1 – a/L)
R2 = wL/2 + W*a/L
Data:
wL:=2 kN; W:=30 kN; L:=8 m; a:=2 m;
Results:
R1 = 23.5 kN
R2 = 8.5 kN
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