14 January 2011

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Mechanics of Materials

CIVL 3322 / MECH 3322

Statics Review

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Statics Review

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A Quiz

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A Quiz

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A Quiz

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A Quiz

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A Quiz

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A Quiz

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Stress and Internal Forces

Statics Review

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¢

In Statics, we spent most of our time

looking at reactions at supports

¢

Two variations from this were when

we considered the forces in trusses

and

¢

The shear and moment at a point in a

beam (you may or may not have

looked at this)

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¢

In Mechanics of Materials, it is these

internal forces and how they affect the

behavior of the system that will be

critical to our analysis

¢

Depending on the loading pattern,

there can vary greatly through the

beam

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Stress and Internal Forces

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¢

At any point in a continuous system,

we can look at the internal forces

acting on the system by modeling the

point we are looking at in the system

as a fixed end support.

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¢

This means that at any point in a

continuous member, we will have a

force parallel to the member, a force

perpendicular to the member and a

resistive moment.

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Stress and Internal Forces

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¢

The force that acts parallel to the cut

we make to separate the member is

known as the axial force or the normal

force

¢

The force that acts perpendicular to

the cut is known as the shear force

¢

The moment is known as the bending

moment

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Stress and Internal Forces

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The dark blue arrows along the axis of

the beam are the axial forces

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¢

The axial force is considered as a

positive axial force if it would cause

the section under consideration to be

in tension.

¢

The axial force is considered as a

negative axial force if it would cause

the section under consideration to be

in compression.

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Stress and Internal Forces

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¢

This shear force is always normal to

the axis of the cut face of the beam

and is typically labeled as V.

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¢

The force acting on the plane of the

cut generates a stress on that plane

¢

If the force is normal to the plane, the

stress is a normal stress or an axial

stress

¢

If the force is parallel to the plane, the

stress is a shear stress

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Stress and Internal Forces

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¢

The magnitude of the stress is the

ratio of the magnitude of the applied

force to the area of the cross section

¢

For normal stress, the expression is

σ

av

g

F

A

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¢

This expression assumes that the

force is equally distributed across the

cut face

¢

To determine the axial stress at a

point required an ability to divide the

force according to some function

σ

av

g

F

A

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Stress and Internal Forces

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¢

Units of stress are similar to units of

pressure

l

Lb

f

/ft

2

l

N/m

2

•

A N/m

2

is given the unit of Pa (Pascal)

σ

av

g

F

A

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¢

Pressure is a scalar, stress is a vector

so they are not exactly the same

¢

Usually you don’t see Pa by itself, the

units are

KPa

,

MPa

,

GPa

σ

av

g

F

A

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Stress and Internal Forces

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¢

Pressure is a scalar, stress is a vector so

they are not exactly the same

¢

Usually you don’t see Pa by itself, the units

are

KPa

,

MPa

,

GPa

E01

A solid 0.5 in diameter steel hanger

rod is used to hold up one end of a

walkway support beam. The force

carried by the rod is 5,000 lb.

Determine the normal stress in the

rod. (Disregard the weight of the rod).

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Rigid bar ABC is supported by a pin at A and axial member (1), which has a cross

section of 540 mm2. The weight of the rigid bad ABC can be neglected.

(a)

Determine the normal stress in member (1) is a load P=8kN is applied at C.

(b)

If the maximum normal stress in member (1) must be limited to 50

Mpa

, what is

the maximum load magnitude P that may be applied to the rigid bar at C?

A 50-mm-wide steel bar has axial loads applied at points B, C, and D. If the normal

stress magnitude in the bar must not exceed 60

MPa

, determine the minimum

thickness that can be used for the bar.

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