Cantilever beam with UVL

Here you will understand how to analyze a cantilever beam with a uniformly varying load and draw shear force and bending moment diagram.

1. by Sk Abdulla Department of Civil Engineering, Murshidabad College of Engineering and Technology Banjetia , Berhampore , 742102, West Bengal, India Introduction to solid mechanics Code – CE 702

2. Analysis of cantilever beam with uvl

3. B A M R W Rx Step 1 : Draw free body diagram

4. Step 2 : Find support Reaction B A M R W ∑ Fy =0 R- ( wl /2) = 0 l ∑M B = 0 M = wl 2 /6 R= wl /2 -( wl /2)*(l/3) + M = 0 ∑ Fx =0 Rx=0 Rx

5. B A M R W x W 1 Now calculate loading intensity at a distance x from point A From the similar triangle condition W/l = W 1 /x W 1 = W*x/l Now shear force at a distance x is nothing but loading area of the small triangle Sx = (1/2)*W1*x = (1/2)*(W*x/l)*x Sx = (Wx 2 /2l) l Step 3 : Calculate shear force

6. B A W x W 1 l Sx = (Wx 2 /2l) At point A when x=0 , from the above equation S A = 0 At point B when x=l , from the above equation S B = Wl /2 B A Wl /2 R SFD M Step 3 : Calculate shear force

7. B A M R W x W 1 Now calculate loading intensity at a distance x from point A From the similar triangle condition W/l = W 1 /x W 1 = W*x/l Now Bending moment at a distance x is nothing but = loading area of the small triangle * perpendicular distance M x = [ (1/2)*W1*x] * (x/3) = [ (1/2)*(W*x/l)*x] * (x/3) M x = (Wx 3 /6l) l Step 4 : Calculate Bending Moment

8. B A M R W x W 1 M x = (Wx 3 /6l) l At point A when x=0 , M A = 0 At point B when x=l , M B = (Wl 2 /6) A B (Wl 2 /6) BMD Step 4 : Calculate Bending Moment

9. Thank You