Cantilever beam with UVL

Cantilever beam with UVL

• 1.
  B Y SK ABDULLA DE PA RT M E N T O F C I V I L E N G I N E E R I N G , M U R S H I D A B A D C O L L E G E O F E N G I N E E R I N G A N D T E C H N O L O G Y B A N J E T I A , B E R H A M P O R E , 7 4 2 1 0 2 , W E S T B E N G A L , I N D I A Introduction to solid mechanics Code – CE 702
• 2.
  Analysis of cantileverbeam 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 ∑MB = 0 M = wl2/6 R= wl/2 -(wl/2)*(l/3) + M = 0 ∑Fx=0 Rx=0 Rx
• 5.
  B A M R W x W1 Now calculateloading intensity at a distance x from point A From the similar triangle condition W/l = W1/x W1 = 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 = (Wx2/2l) l Step 3 : Calculate shear force
• 6.
  B A W x W1 l Sx =(Wx2/2l) At point A when x=0 , from the above equation SA = 0 At point B when x=l , from the above equation SB = Wl/2 B A Wl/2 R SFD M Step 3 : Calculate shear force
• 7.
  B A M R W x W1 Now calculateloading intensity at a distance x from point A From the similar triangle condition W/l = W1/x W1 = W*x/l Now Bending moment at a distance x is nothing but = loading area of the small triangle * perpendicular distance Mx =[ (1/2)*W1*x] * (x/3) = [(1/2)*(W*x/l)*x] * (x/3) Mx = (Wx3/6l) l Step 4 : Calculate Bending Moment
• 8.
  B A M R W x W1 Mx =(Wx3/6l) l At point A when x=0 , MA = 0 At point B when x=l , MB = (Wl2/6) A B (Wl2/6) BMD Step 4 : Calculate Bending Moment