Shear Moment and Deflection Diagrams for BEAMS

Adapted from [?] 1) Simple Beam; uniform Load

w L

III

Vx at center M,

5 wL4 384 EI

2) Simple Beam; Unsymmetric Triangular Load

Ri e

*_IMMttttt^

t Shear

Max R2 = V2 Vx at x = .577L Mmax Mx at x = .5193L Amax Ax

.1283WL

.01304 WL

Wx3 180EIL2

Moment

Shear

Moment

3) Simple Beam; Symmetric Triangular Load

3) Simple Beam; Symmetric Triangular Load

Triangular Loading Beam Moment
4) Simple Beam; Uniform Load Partially Distributed

B, t

w

-c-►

1

—-x-

ll In,

Shear

V,

1

a + R, /w —

H.

1

V,

I

M 1 '

.mil

1

111,

Moment

Max when a < c

Ri — Vi — wL (2c

+ b)

Max when a > c

R2 — V2 — Wt (2a

+ b)

when a < x < a + b

Vx

— Ri — w(x — a)

when x < a

Mx

— Ri x

when a < x < a + b

Mx

— Ri x —

■ w (x - a)2

when a + b < x

Mx

— R2 (L

w

Mmax

' 2w/

5) Simple Beam; Concentrated Load at Center

Shear at x — 2 when x < 2 whenx < 2 at x — L

Mmax

Mx Ax

Amax

4 Px

48EI PL3 48EI

Moment max

6) Simple Beam; Concentrated Load at Any Point

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