lecture 5 introduction to engineering approximate running time - 15 minutes
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Lecture 5 Introduction to Engineering Approximate Running Time - 15 minutes Distance Learning / Online Instructional Presentation Presented by Department of Mechanical Engineering Baylor University Procedures: - PowerPoint PPT PresentationTRANSCRIPT
Slide 1 © 2006 Baylor University
EGR 1301
Lecture 5Introduction to Engineering
Approximate Running Time - 15 minutesDistance Learning / Online Instructional Presentation
Presented byDepartment of Mechanical Engineering
Baylor University
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Slide 2 © 2006 Baylor University
EGR 1301
Introduction to Static Analysis – Part 2
EGR 1301 – Lecture 5
Prof. Dick Campbell Speaking
Slide 3 © 2006 Baylor University
EGR 1301
Learning Objectives
• Understand the concept of Force as a vector.• Understand separating a vector into
components.• Apply this concept to analyzing sums of Forces.• Determine the load in structural elements.• Understand the concept of a “Factor of Safety”.
Slide 4 © 2006 Baylor University
EGR 1301
Force as a Vector
• Forces – Have magnitude and direction– in an x-y coordinate system, the force may be broken
down into “components” along the coordinate axes.
•The magnitude of a vector can be found by the magnitude of its components using Pythagorean theorem.
x
y
F
xF
yF
22yx FFF
Slide 5 © 2006 Baylor University
EGR 1301
Setting Up the Analysis
• Draw a sketch of the Forces• Write each force in terms of i and j components (components
perpendicular to each other can be treated separately) • Sum of i and j components = zero (Newton’s 1st Law)• Solve two equations, two unknowns• Find tension force in cable• Calculate safety factor
x
y
1F
xF1
yF1
jFiFF yxˆˆ
111
i
j
jFiFF yxˆˆ
222
2F
Slide 6 © 2006 Baylor University
EGR 1301
Force Vectors and Static Analysis
• Consider the foot bridge– Loaded by six persons (approx. 1000 lbs)– Loaded at the center of the bridge
• Simplifying assumption:– Neglect the weight of the bridge
lbsF 10003
?1 F ?2 F
i
j
ft 130
ft 5
Slide 7 © 2006 Baylor University
EGR 1301
• Resolve the three forces into i,j components.
• Our unknowns are F1 and F2.
• Since the i,j directions are independent, we can solve these two equations for the unknowns
Static Analysis of the Bridge Cable
lbsF 10003 ?1 F
?2 F
ft 130
ft 5)(tan 4.4 65
51 o
jiF ˆ1000ˆ03
jfifF ˆsinˆcos 222
jfifF ˆsinˆcos 111
so, 0321 FFF
0ˆ0ˆcosˆcosˆ21 iififiF
0ˆ1000ˆsinˆsinˆ21 jjfjfjF
Slide 8 © 2006 Baylor University
EGR 1301
Static Analysis of the Bridge Cable (cont.)
0ˆ0ˆcosˆcosˆ21 iififiF
0ˆ1000ˆsinˆsinˆ21 jjfjfjF
substituting:
2121 ),4.4cos()4.4cos( ffff
1000)4.4sin()4.4sin( 21 ff
lbs 651721 ff
Safety Factor (Cable Strength - 16,000 lbs):
46.2lbs 6517
lbs 16000.. FS
Slide 9 © 2006 Baylor University
EGR 1301
Static Analysis of the Bridge Cable (cont.)
Then: 1000)10sin(2 1 f lbs 287921 ff
56.5lbs 8792
lbs 16000.. FS
What happens to the Safety Factor if we increase the sag? Let o10
What happens to the Safety Factor if we include the weight of the bridge? Let lbs 600 and 10 Wo
Then: 1600)10sin(2 1 f lbs 460721 ff
47.3lbs 6074
lbs 16000.. FS
Slide 10 © 2006 Baylor University
EGR 1301
Homework Assignment #1Problem #1
Given a load of 500 N (Newtons) supported by two cables as shown, determine the force in each cable.
N 500
?1 F
?2 F
i
j
m 20
m 5
m 5
Slide 11 © 2006 Baylor University
EGR 1301
Homework Assignment #1Problem #2
Given
?1 F
?2 Fi
j
m 8
m 5
magnitude N 1000ˆ447ˆ8943 jiF
m 10
m 10
m 4
3F
Determine the required forces (magnitudes) in cables 1 & 2 so that the system will remain in static equilibrium.
Slide 12 © 2006 Baylor University
EGR 1301
This Concludes Lecture 5