Draft

Shear max when a K h max when a > h at x = a when x K a at x = a when x K a at x = \J & a > h

Mmax

Mx Aa Ax

Pb L Pa

L Pbx L

Pa2b2

3EIxL

Moment

7) Simple Beam; Two Equally Concentrated Symmetric Loads

Shear

Moment

P Pa

8) Simple Beam; Two Equally Concentrated Unsymmetric Loads

L

1

—— x —-

p

p

1

--b--

V(

t

Shear

v2

1

I

„ml

lllll,

Moment

max when a < b

Rl =

Vl

= L (L

-a + h)

max when b < a

R2 =

V2

= L (L

-h + a)

when a < x < L — b

Vx

= L (h-

- a)

max when b < a

M1

= Rl a

max when a < b

M2

= R2 h

when x < a

Mx

= Rl x

when a < x < L — b

Mx

= RiX

— P (x -

9) Cantilevered Beam, Uniform Load

Mmax

Amax

48EI wL4 185EI

Moment wx

10) Propped Cantilever, Concentrated Load at Center

Moment

10) Propped Cantilever, Concentrated Load at Center

1

-.-I _

P

--L / 2--

-—L ,/ a

: K2

V,

^rfflTiïiïÏÏÏÏli Moment

when x < Ll Mx = 5Pf 1 when L < x Mx = P(L - ±6) Jmax' at x = .4472L Amax = .009317E3

11) Propped Cantilever; Concentrated Load

11) Propped Cantilever; Concentrated Load

Ri r

Shear

Moment

when a < .414L at x when .414L < a at x =

R1 =

V1 =

R2 =

V2 =

at

x=a

M1

=

at

x=L

M2

=

at

x=a

Aa

=

L L2 + a2 L SL2-a2

Amax

=

L

a

Amax

/ 2L+a

6EI V 2L+a2

6EI V 2L+a2

12) Beam Fixed at Both Ends, Uniform Load

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