ENGINEERING MECHANICS-«STATICS EC3221
FALL 2011
EXAM 2
October 14, 2011
Name St) I off} 0 m5
please print
Signature
SU Identification No.
Recitation instructor
Recitation Day
Problem #1
Pr
Engineering Mechanics
Statics
ECS221
A. J. Levy
Course Structure
M,W lecture + F clinic or exam
Graded homework (13%)
Four class exams (54%)
Final exam (33%)
Course evaluation
Introduction
Primiti
Rectangular Components; Unit
Vectors
Rectangular Components
y
y
F
=
x
Fy
Fx
x
Unit Vectors
A vector directed along the positive x or y axis
with unit magnitude.
Fx = Fxi , Fy = Fyj
y
F = Fx + Fy
F =
Rigid Bodies; Equivalent Force
Systems
Transmissibility Principle
F
=
Force F is a sliding vector.
F
Vector (Cross) Product
Multiply 2 vectors PQ resulting in a
vector.
Define magnitude of product.
REVIEW PROBLEMS for Midterm Exam 2
(PHY212)
(Mostly from Recitation Sessions)
SELF STUDY: Related Conceptual Questions on Chapters 27,28, and 29.
1.
EX27.19
The figure below shows three Gaussian surfa
Couples
A system of 2 forces of equal magnitude parallel
lines of action and opposite sense.
The Couple
F
-F
Moment of a Couple
MO = rAF + rB(-F) = (rA- rB) F = rF
-F
rB
rA
O
r
F
Moment of a couple:
M
Engineering Mechanics
Statics
ECS221
A. J. Levy
Course Structure
M,W lecture + F clinic or exam
Graded homework (13%)
Four class exams (54%)
Final exam (33%)
Course evaluation
Introduction
Primitive c
ECS 221: Engineering Mechanics
Trusses Method of Joints
Lecture 23
Truss Analysis - Basics
Very Efficient Structural Solution for
spanning long distances
All joints are pins, thus no moments
All me
Principle of Virtual Work II
Recall: work done by force F in
incremental displacement dr is
dU = Fdr = F dr cos
For a finite displacement:
2
2
2
1
1
1
U 12 = dU = F dr = Fcos dr
2
1
Examples
F consta
PRODUCTS OF INERTIA
I
Product of inertia: xy = xy dA
y
Ixy may not be
positive!
A
x
y
x
The Rectangle
Compute Ixy.
dA = dxdy
dIxy = xydxdy
y
b
I xy = xdx ydy
0 0
h
dy
h
b
x
122
I xy = b h
4
Geometric
Principle of Virtual Work I
The principle of virtual work is an
alternative formulation of the
principles of equilibrium. It is often
more convenient to use since it
effectively eliminates forces of
c
The Parallel Axis Theorem
The parallel axis theorem is used with
the method of composite parts.
y
y
x
y
x
x
If Ix is known for centroidal axis how to get
it for any other parallel axis?
Theorem: I = I
MOMENTS OF INERTIA
Distributed forces act on volume or
surface elements.
Gravity
Hydrostatic pressure in a fluid
Bending stress in beams
Center of Gravity for Area
Center of gravity
W = t A
W = dW x