14mmL

16m12m1 + m22L16mmL

12mmL

m21L + a241

12mm a3 + 3a

L-a2

L2bL1

6m3m11L + b2 +16mm1L + a2

12mmL

+ m21m1 + 2m224L1

123m13m1 + 5m224L16 3m112m1 + m22

16m1m1 + 2m22L12m1m1 + m22L

512mmL

16m1m1 + 2m22L13mmL

12mmL

23mmL

12m1m1 + m22L12mmLmmL

LL

0mm dx

Table for Evaluating m m dxLL

0

Beam Deflections and Slopes

Loading Equation

at x = Lat x = L

v =MO2EI

x2umax =MOL

EIvmax =

MOL2

2EI

at x = Lat x = L

v =P

6EI1x3 - 3Lx22umax = -PL

2

2EIvmax = -

PL3

3EI

gcgu +cv +

Beam Deflections and Slopes (continued)

v = -MOx

6EIL1L2 - x22

uR =MOL

3EI

vmax = -MOL

2

923EI

uL = -MOL

6EI

L>2 x Lv = -

wL384EI

18x3 - 24Lx2 + 17L2x - L32uR =7wL3

384EI

0 x L>2uL = - 3wL3

128EI

v = -wx

384EI116x3 - 24Lx2 + 9L32

at x =L

2

v = -wx

24EI1x3 - 2Lx2 + L32umax =

wL3

24EIvmax = -

5wL4

384EI

0 x au =Pab1L + a2

6LEI

v = -Pbx

6LEI1L2 - b2 - x22uL = -Pab1L + b26LEI

0 x L>2at x = 0 or x = Lat x = L>2v =

P

48EI14x3 - 3L2x2,umax = PL

2

16EIvmax = -

PL3

48EI

at x = Lat x = L

v = -w

24EI1x4 - 4Lx3 + 6L2x22umax = -

wL3

6EIvmax = -

wL4

8EI