ENGR 225Section 1.1 -1.2

Mechanics of Materials

Mechanics of Solids

Mechanics of Deformable Bodies

Solid Mechanics

Strength of Materials.

Statics

Forces

Rigid Bodies

Dynamics

Motion

Particles, Rigid Bodies

Mechanics of Materials

Forces External

Internal

Material Properties

Mechanics of Materials

• Area of mechanics that studies the relationships between external loads applied to a deformable body and the intensity of internal forces within a body

• An understanding of material behavior will play an important role in developing the necessary equations used in mechanics of materials.

Support Reactions

Internal Forces

Method of Sections

Internal Forces in 2-D

Determine the internal forces (normal force, shear force and bending moment) on a section passing

through the beam at point C.

Internal Forces in 3-D

Internal Forces in 3-DFind the internal forces at the base

Mass = 650 kg and Wind Load = 900 N/m2

Internal Forces at a point – method of Sections

Internal forces at all points along length

Internal forces – a function of distance along length of beam.

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 we are primarily concerned about shear and bending failures.

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 an internal moment that causes a compression or pushing on the upper part of the member

Relations between Distributed Load, Shear, and Moment.

• Slope of the Shear Diagram = Negative of distributed load intensity

• Slope of the bending moment diagram = Shear

)(xwdx

dV V

dx

dM

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