Transcript Computer Aided Design

Static Analysis
Static Analysis, Internal Forces, Stresses: Normal and Shear
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Static Analysis
Equation of equilibrium
F
x
M
x
0
0
F
0
y
M
y
0
F
z
M
z
0
0
If only x-y plane
F
x
0
F
y
0
M  0
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Types of Connection
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Think!
Lecture 2
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FBD: Structure
Discuss the approach?
Lecture 1
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i) Equilibrium on the whole system
iii) Equilibrium on Pin C
ii) Equilibrium on Pin A
iv) Equilibrium on Pin D
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Take Note of the tension and compression on the members
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Two and three force body member
Three-Force
member
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Two force member
determination will set the
direction of FAB
Then, equilibrium equation will solve FBD: FAB, Cx and Cy
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Find the forces on each member
Discuss the approach?
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Method 1: From Pin to Pin (equilibrium)
Statics and Mechanics of Materials, Third Edition
Russell C. Hibbeler
Copyright ©2011 by Pearson Education, Inc.
All rights reserved.
Question:
Can we solve the problem by treating the whole system
as the initial FBD?
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Discuss the approach?
Use your engineering judgment?
1) What is the direction of the force at
Use your engineering judgment?
C?
Does length of frame has the effect on 2) If the downward force 0.75P is
the force calculation?
removed, which frame should be
removed?
Lecture 1
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Try! (FBD)
Draw the FBD if P = 1500 N
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Solution
FBD = 5905.36 N
Cx = 2952.68 N
Cy= 3614.20 N
C = 4666.98 N
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Discuss the approach?
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Internal Forces
Considering the external and
internal forces; the most
critical is PBC = 30 kN.
Therefore, by knowing the
external and internal forces,
we can decide the most
critical part to be further
analyzed.
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Internal Forces
Find the internal
forces at point E
Solve the FBD first
m = 500 kg
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M
A
0
solve FCD
F
X
0
F  0
Y
Solve Ax and Ay
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Internal Forces
M
E
0
solve ME
F
X
0
F  0
Y
Solve VE and NE
Similar from Point B to E, apply the equilibrium
equation to calculate the internal forces
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Internal Forces: Example
Example 1.1
Calculate the
VC, NC and MC
and their
direction
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Normal Stress
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 ave
P

A
P: force that is perpendicular to plane
( the force is acted on the center of designated area)
A: area of the plane
Calculate the average normal stress:
d = 200 mm
Structure (Assume P = 100 kN )
Wide Flange Structure: W310 x 74
Angles L203 x 203 x 19.0
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Allowable Normal Stress
• The allowable stress is the maximum stress allowed due to the
properties of the material.
 all   ave
Considered as SAFE
 all   ave
Considered as FAIL
 all
F .S 
 ave
Safety Factor
Safe F.S >= 1
Fail F.S < 1
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Solve it
A load W is supported by a 3‐cable system
as shown in figure 1. The cable run along 2
pulleys F and D which is attached to the
solid wall by a round beam EF and CD both
of which are 30mm diameter and 300mm
long. Ignore the mass of cable and beam.
All
cables are the same size. The sizes of the
pulleys at D & F can be ignored. Gravity =
9.81m/s2
Answer the following questions:
1.Find the internal stress at the mid point
of round beam FE
2.Calculate the normal stresses at cable
AB, BD, BF
3.Calculate the diameter of the cable is the
allowable stress is 140 MPa
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