engr 220 section 6.1~6.2 bending. internal forces

ENGR 220Section 6.1~6.2

BENDING

Internal Forces

Method of Sections

Internal Forces in 2-D

Shear and Moment Diagrams

• For beams we can calculate the shear and moment diagrams as a function of position along the beam.

• Internal normal force will not be considered in that most loadings are vertical on a beam and were are primarily concerned about shear and bending failures.

Graphical Method for Shear and Bending Moment Diagrams

Vdx

dM

xwdx

dV

)(

Sign Convention

• Shear ~ positive direction is denoted by an internal force that causes a clockwise rotation on which it acts.

• Moment ~ positive direction is denoted by and internal moment that causes a compression or pushing on the upper part of the member

Graph the internal forces shear force and bending moment along the axis of the beam.

Problem 7-11

-30

-20

-10

0

10

20

30

40

50

60

70

0 5 10 15

Position along the beam

Sh

ear

Fo

rce

(kip

) o

r B

end

ing

Mo

men

t (k

ip f

t)

Shear Force

Bending Moment

7-87: Draw the shear and loading diagrams

Problem 7-87

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

0 2 4 6 8 10 12

Position on Beam

Sh

ear

(kip

) o

r M

om

ent

(kip

*ft)

ShearBending Moment