Page 37 - Mechanical Engineer's Data Handbook

26 MECHANICAL ENGINEER’S DATA HANDBOOK

Symbols used: Maximum bending moment M, = k, WL
L = length of beam Maximum slope i, = k, WL2/EI
I =second moment of area Maximum deflection y, = k3 WL3/EI
w = load per unit length
W= total load = WL for distributed loads
E =Young’s modulus

Moment coefficient, Slope coefficient, Deflection coefficient,
Type of beam kl k2 k3
1
1 - 1 -
3
2
at wall at load at load

1
1
- - 1 -
2 6 8
at wall at free end at free end

1
1 - - I -
u2 1 u2 4 16 48
at load at ends at load

F K(l -K) K( 1 - K2)/6 K2( 1 - K)’/3

KL at load at right-hand end at load
I
I for K>f (not maximum)
L

5
1
- 1 - -
8 24 384
at centre at ends at centre
L
1 - 1 - -
1
8 64 192
at centre and ends at ends at centre

1 - -
1
12 0.00803 384
at ends at 0.21 1 L from each end at centre