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BEAM DEFLECTION FORMULAE
BEAM TYPE SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM DEFLECTION
1. Cantilever Beam – Concentrated load P at the free end
2
2
Pl
EI ! " #
2
36
Pxy l x
EI! $
3
max3
Pl
EI% !
2. Cantilever Beam – Concentrated load P at any point
2
2
Pa
EI !
" #2
3 for 06
Pxy a x x a
EI! $ & &
" #2
3 for6
Pay x a a x l
EI! $ & &
" #2
max 36
Pal a
EI% ! $
3. Cantilever Beam – Uniformly distributed load (N/m)
3
6
l
EI
' ! " #
22 26 4
24
xy x l lx
EI
'! ( $
4
max8
l
EI
'% !
4. Cantilever Beam – Uniformly varying load: Maximum intensity o (N/m)
3
o
24
l
EI
' ! " #
23 2 2 3o 10 10 5
120
xy l l x lx x
lEI
'! $ ( $
4
omax
30
l
EI
'% !
5. Cantilever Beam – Couple moment M at the free end
Ml
EI !
2
2
Mxy
EI!
2
max2
Ml
EI% !
BEAM DEFLECTION FORMULAS
BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER
DEFLECTION
6. Beam Simply Supported at Ends – Concentrated load P at the center
2
1 216
Pl
EI ! !
223
for 012 4 2
Px l ly x x
EI
) *! $ & &+ ,
- .
3
max48
Pl
EI% !
7. Beam Simply Supported at Ends – Concentrated load P at any point
2 2
1
( )
6
Pb l b
lEI
$ !
2
(2 )
6
Pab l b
lEI
$ !
" #2 2 2 for 06
Pbxy l x b x a
lEI! $ $ & &
" # " #3 2 2 3
6
for
Pb ly x a l b x x
lEI b
a x l
/ 0! $ ( $ $1 23 4& &
" #3 22 2
max9 3
Pb l b
lEI
$% ! at " #2 2 3x l b! $
" #2 2 at the center, if 3 448
Pbl b
EI% ! $ a b5
8. Beam Simply Supported at Ends – Uniformly distributed load (N/m)
3
1 224
l
EI
' ! ! " #3 2 32
24
xy l lx x
EI
'! $ (
4
max
5
384
l
EI
'% !
9. Beam Simply Supported at Ends – Couple moment M at the right end
16
Ml
EI !
23
Ml
EI !
2
21
6
Mlx xy
EI l
) *! $+ ,
- .
2
max9 3
Ml
EI% ! at
3
lx !
2
16
Ml
EI% ! at the center
10. Beam Simply Supported at Ends – Uniformly varying load: Maximum intensity o (N/m)
3
o1
7
360
l
EI
' !
3
o2
45
l
EI
' !
" #4 2 2 4o 7 10 3360
xy l l x x
lEI
'! $ (
4
omax 0.00652
l
EI
'% ! at 0.519x l!
4
o0.00651l
EI
'% ! at the center