# Mechanics of Materials

Μηχανική

18 Ιουλ 2012 (πριν από 5 χρόνια και 10 μήνες)

443 εμφανίσεις

14 January 2011
1
Mechanics of Materials
CIVL 3322 / MECH 3322

Statics Review
Response Card Registration
Statics Review
2
14 January 2011
2
Response Card Registration
Statics Review
3
Response Card Registration
Statics Review
4
14 January 2011
3
Response Card Registration
Statics Review
5
Response Card Registration
Statics Review
6
14 January 2011
4
Response Card Registration
Statics Review
7
Response Card Registration
Statics Review
8
14 January 2011
5
Response Card Registration
Statics Review
9
Response Card Registration
Statics Review
10
14 January 2011
6
A Quiz
Statics Review
11
A Quiz
Statics Review
12
14 January 2011
7
A Quiz
Statics Review
13
A Quiz
Statics Review
14
14 January 2011
8
A Quiz
Statics Review
15
A Quiz
Statics Review
16
14 January 2011
9
Stress and Internal Forces
Statics Review
17
¢

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)
Stress and Internal Forces
Statics Review
18
¢

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

¢

there can vary greatly through the
beam
14 January 2011
10
Stress and Internal Forces
Statics Review
19
¢

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.
Stress and Internal Forces
Statics Review
20
¢

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.
14 January 2011
11
Stress and Internal Forces
Statics Review
21
¢

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
Stress and Internal Forces
Statics Review
22
14 January 2011
12
Stress and Internal Forces
Statics Review
23
¢

The dark blue arrows along the axis of
the beam are the axial forces
Stress and Internal Forces
Statics Review
24
¢

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.

14 January 2011
13
Stress and Internal Forces
Statics Review
25
¢

This shear force is always normal to
the axis of the cut face of the beam
and is typically labeled as V.
Stress and Internal Forces
Statics Review
26
¢

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
14 January 2011
14
Stress and Internal Forces
Statics Review
27
¢

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
Stress and Internal Forces
Statics Review
28
¢

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
14 January 2011
15
Stress and Internal Forces
Statics Review
29
¢

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
Stress and Internal Forces
Statics Review
30
¢

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
14 January 2011
16
Stress and Internal Forces
Statics Review
31
¢

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).
14 January 2011
17
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.