Explanation:
To find maximum deflection expression.
Students are advised to memorise the standard results. This
δ= is a standard result for cantilever beam with UVL.
For derivation of formula refer this
Here
w= per unit length at a distance
x from
O ∴
EI=− EI=−+C1 S.F. is zero at x = 0, giving
C1 = 0
∴
EI=− ∴
EI=−+C2 B.M. is zero at x = 0, giving
C2 = 0
EI=− Integrate again
EI=−+C3 But
=0 at
x=L, giving
0=−+C3 i. e,
C3= y=(L4x−)+C4 Now y = 0 at x = L, giving
C4=−=− ∴
y=(L4x−)− y=−(4L5−5L4x+x5) Since the deflection will be maximum at the end O i.e. at x = 0, put this in the above
obtained expression to get
δ=, where negative indicates the deflection is towards negative
y axis.