## 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

 1 —— x —- p p 1 --b-- V( t Shear v2 1 I „ml lllll,
 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 -

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

Ri r

Shear

Moment

 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

0 0