ATENEO CENTRAL BAR OPERATIONS 2007
Political Law
SUMMER REVIEWER
CONSTITUTIONAL LAW . 2
ARTICLE I THE NATIONAL TERRITORY . 2
ARTICLE II DECLARATION OF PRINCIPLES AND STATE POLICIES. 2
ARTICLE III BILL OF RIGHTS . 4
ARTICLE IV CITIZENSHIP . 23
ARTICLE V SU

Meeting 11
Angle of Twist, Statically determinate and indeterminate torsion
members
Angle of Twist
=
Where:
Angle of Twist
T Torque
L Length
J Polar Moment of Inertia
G Shear Modulus of Elasticity
*In torque, clockwise is positive
while counter-clockwis

Meeting 20
Combined Loading
Stresses in a cross-sectional area
Normal Stress:
=
Shear Force:
=
Flexure Stress:
=
Superposition
Problem 1
Determine the normal stress
developed at corners A and B of
the column.
Problem 2
Determine the state of stres

Meeting 12
Equilibrium of Beam: Types of Supports, Types of Beams, Shear and
Bending Moment Equations; Shear and Bending Moment Equations
Types of Support
Types of Beams
Shear and Bending Moment in a Beam
Problem 1
Express the shear and moment
functions

MEDEFOR Q1
PROBLEM 1
Given: Area (mm2 ) E (GPa) L (m)
Al
200
70
2
Br
300
83
4
St
500
200
4
a.) What is the magnitude of the internal force along the bronze cord?
b.) What is the magnitude of elongation occurring at the steel cord?
c.) What is the magnitud

Meeting 6
Statically Indeterminate Axially Loaded Memebrs
Statically Indeterminate Members
When the reactive forces or the
internal resisting forces over a
cross section exceed the number of
independent equations of
equilibrium, the structure is called
s

Meeting 8
Review
Problem 1
A homogenous 150 kg bar AB
carries a 2 kN force as shown in the
figure. The bar is supported by a pin
at B and a 10 mm diameter cable
CD. Determine the stress in the
cable.
Answer: S = 87.08MPa
Problem 2
A 750 mm pulley, load

Meeting 7
Thermal Stress
Thermal Stress
A change in temperature can cause a body to
change its dimensions. Generally, if the
temperature increases, the body will expand,
whereas if the temperature decreases, it will
contract. Ordinarily this expansion or

Meeting 2
Simple Stresses: Normal Stress under Axial Loading, Shearing Stress
Dont be stress with stress
Reference: mathalino.com
Strengths of Materials
Strength of Materials (also known as Mechanics of Materials) is the
study of the internal effect of e

Meeting 10
Torsional Shear Stress, Torsional Deformation, Power Transmission
Torsional Deformation
Torsional Shear Stress
=
Where:
T Torque
Shear Stress
Radius
J Polar Moment of Inertia
Polar Moment of Inertia
General Equation:
=
2
0
For Solid Sh

Meeting 5
Tension and Compression Test; Stress-Strain Diagram; Hookes Law; Strain
Energy; Poissons Ratio; Elastic Deformation of an Axially Loaded Member
Reference: Hibbeler (2011)
Tension and Compression Test
Stress-Strain Diagram
Elastic Behavior
Elas

Meeting 3
Bearing Stress; Stresses on Inclined section; Allowable Stress Design
Reference: mathalino.com; setareh.arch.vt.edu
Problem 1
Two block of wood, 50mm wide and 20mm thick, are glued together
as shown in the figure. Using the free-body diagram co

Meeting 4
Deformation; Normal Strain; Shear Strain; Hookes Law
Normal Strain
Change in length of a
material per unit length
Where:
unit deformation or strain
n elongation length along
the normal axis
L length of material
=
Problem 1
The corners B an

Meeting 24
Review for Quiz 3
Problem 1
The state of stress at a point is
shown
on
the
element.
Determine (a) the principal
stress and (b) the maximum inplane shear stress and average
normal stress at the point.
Specify the orientation of the
element in e

MOMENTS
1.)
The 4-kN force F is applied at point A. Compute the moment of F about point O,
expressing it both as a scalar and as a vector quantity. Determine the coordinates of
the points on the x- and y-axes about which the moment of F is zero.
[
(
)
(
)

IMPACT: International Journal of Research in
Engineering & Technology (IMPACT: IJRET)
ISSN(E): 2321-8843; ISSN(P): 2347-4599
Vol. 2, Issue 2, Feb 2014, 259-264
Impact Journals
GREEN CONCRETE: EFFICIENT & ECO-FRIENDLY CONSTRUCTION MATERIALS
CHIRAG GARG &

Properties of Exponents
An exponent (also called power or degree) tells us how many times the base will be multiplied by itself. For
example , the exponent is 5 and the base is . This means that the variable will be multiplied by itself 5 times. You
can a

Note: Cover Page (Print)
Note: 8.5 x 11
De La Salle University Dasmarias
College of Engineering, Architecture, and Technology
(_) Engineering Program
Font: Garamond
Font Size: 14pt
PRELIM/MIDTERM/FINALS PROBLEM SET
Font: Garamond
(ALL CAPS) (Bold)
Font Si

Differential Equations
START by doing what's necessary;
then DO WHAT'S POSSIBLE;
and suddenly you are doing
the impossible.
Saint Francis of Assissi
OUTLINE
Differential Equations
Definitions
Elimination of Arbitrary Constants
First Order DE
Higher or

Differential Equations
ENGM316 Differential Equations with Engineering Applications
For where your treasure is, there your heart
will be also.
~ Luke 12:34
2
Agenda
Pass Assignment, Friction Pen, PS Format
Exact DE
Linear DE
Bernoulli Equation
3
Summa

Midterm: Application of DEs
ENGM316 Differential Equations with Engg Applications
Martha, Martha, you are worried and troubled
about many things. But one thing is needed, and
Mary has chosen that good part, which will not be
taken away from her.
~ Luke 1

PROB. SET #1
1.
MEDEFOR
The lap joint shown is fastened by two 20mm diameter rivets. If P = 50 KN and the
thickness of each plate is 25mm, determine : a.) the shearing stress in each rivet b.) the
bearing stress in each plate and c.) the maximum tensile s

Meeting 22
Stress Transformations; General Equations of Plane Stress; Maximum InPlane Stress; Principal Stress; Mohrs Circle
Stress Transformation
General State of Stress
Plane Stress
Plane Stress
Plane Stress
General Equations of Plane Stress
General Equ

Meeting 15
Shear Stress in Beams
Shear Stress in Beams
Shear Stress in Beams
= 0
= 0
+
= ()
1
=
=
= 0
Where
=
- distance from the centroid of the portion to the
neutral axis
- area of the portion
Problem 1
If the beam is subjected to a
shea

Mechanics of Deformable Bodies:
Thin-walled Pressure Vessel
Thin-walled Pressure Vessel
Tangential Stress
Longitudinal Stress
Engr. Lydia Francisca D. Florentino
Assistant Professor
Pressure Vessel
It refers to a tank or pipe carrying a fluid or gas
u

Mechanics of Deformable Bodies:
Combined Loads and Stresses
Combined Axial and Torsional Loads
Combined Axial and Flexural Loads
Combined Bending and Torsion
Engr. Lydia Francisca D. Florentino
Assistant Professor
Three basic types of loading:
P
Axia

Mechanics of Deformable Bodies:
Plane Stress Transformation
Engr. Lydia Francisca D. Florentino
Assistant Professor
Stress at a General Point in
Arbitrarily Loaded Body
Stresses acting on an x plane at point Q in the body.
Stress at a General Point in
A

From outline 2
Hydropower is powering machinery for example a turbine to generate electricity with
the use of water as it's prime mover and because water is constantly revitalized hydropower is
consider to be a renewable energy("How Hydropower Works," 201

CALAMBA STEEL CENTER, INC.
About:
CALAMBA STEEL CENTER, INC. is a steel service center that slits, levels, shears and re-shears flat
steel products.
History
The original company, JS Steel Corporation was incorporated on Oct 1989 as a joint venture
between