CE 221 Homework 1 & 2 Due Wednesday September 15, 2010
1.
Proof the following trigonometric identity:
Tan(2a ) =
2.
2 tan a 1 tan 2 a
Proof that sin(a+b) = [sin(a)][cos(b)] + [cos(a)][sin(b)] Proofs that for any triangle, the following ratios are equal (t
CENTROID & MOMENTS OF INERTIA INERTIA
Centroid And Moment Of Inertia For Composite Areas
LEARNING OBJECTIVES LEARNING
Be able to apply the parallel-axis Be
theorem theorem Be able to determine the moment of Be inertia for composite areas inertia
PRE-REQU
INTRODUCTION AND REVIEW REVIEW
ME 221 STATICS ME
CE 221 Statics
ME 222 Mechanics of Deformable Solids
CE 305 CE 312 CE 321 CE 337
ME 423 ME 425 ME 426 ME 477 ME 495
GENERAL REVIEW GENERAL
Trigonometry
GEOMETRY/TRIGONOMETRY GEOMETRY/TRIGONOMETRY
a b a b
b
RIGID BODY EQUILIBRIUM 3-D EQUILIBRIUM
Equilibrium of Rigid Body in 3-D Equilibrium
LEARNING OBJECTIVES LEARNING
Be able to identify support reactions in Be
3-D and draw a free body diagram 3-D Be able to identify an indeterminate Be system system Be abl
STRUCTURAL ANALYSIS
Method Of Joints Method
LEARNING OBJECTIVES LEARNING
Be able to define a simple truss Be able to determine the forces in Be
members of a simple truss using the method of joints the Be able to identify the zero-force Be members members
RIGID BODY EQUILIBRIUM EQUILIBRIUM
Rigid Body Equilibrium 2-D Rigid
LEARNING OBJECTIVES LEARNING
Be able to recognize two-force Be
members members Be able to apply equations of Be equilibrium to solve for unknowns equilibrium
PRE-REQUISITE KNOWLEDGE PRE-
STRUCTURAL ANALYSIS
Method of Sections Method
LEARNING OBJECTIVES LEARNING
Be able to determine the forces in Be
members of a simple truss using the method of sections
PRE-REQUISITE KNOWLEDGE PRE-REQUISITE
Units of measurement Trigonometry concepts Rect
STRUCTURAL ANALYSIS ANALYSIS
Frames and Machines Frames
LEARNING OBJECTIVES LEARNING
Be able to draw the free body Be
diagram of a frame or machine and its members its Be able to determine the forces acting Be at the joints and supports of a frame or mac
INTERNAL FORCES INTERNAL
Internal Forces Developed in Structural Members Members
LEARNING OBJECTIVES LEARNING
Be able to use the method of sections for Be determining internal forces in 2-D load case determining
PRE-REQUISITE KNOWLEDGE PRE-REQUISITE
Units
Michigan State University Department of Civil and Environmental Engineering CE 221 Statics (3 credits) CE
Spring 2010 Maximum time allowed is 50 minutes Note: - This is a closed book and notes test. You are prohibited from using stored formulae and/or pro
INTERNAL FORCES FORCES
Shear Force and Bending Moment Equations and Diagrams Equations
LEARNING OBJECTIVES LEARNING
Be able to draw shear force and Be
bending moment diagrams for beams beams
PRE-REQUISITE KNOWLEDGE PRE-REQUISITE
Units of measurement Tri
Michigan State University
Department of Civil and Environmental Engineering
CE 221 Statics (3 credits)
Spring 2014
Sample Final Exam
Maximum time allowed is 120 minutes
The problems on the final exam will be selected from the
practice problems, class exam
CENTER OF GRAVITY AND CENTROID
Composite Bodies Composite
LEARNING OBJECTIVES LEARNING
Be able to determine the location of Be
the center of gravity, center of mass, or the centroid using the method of composite bodies
PRE-REQUISITE KNOWLEDGE PRE-REQUISI
MOMENT OF INERTIA
Moment of Inertia by Integration Moment
LEARNING OBJECTIVES LEARNING
Be able to define the moment of Be
inertia for an area inertia Be able to determine the moment of Be inertia for an area by integration inertia Be able to determine th
FRICTION
Dry Friction Dry
LEARNING OBJECTIVES LEARNING
Be able to understand the Be
characteristics of dry friction characteristics Be able to draw a FBD including Be friction friction Be able to solve problems Be involving friction involving
PRE-REQUISI
INTERNAL FORCES FORCES
Relationships Between Load, Shear and Bending Moment and
LEARNING OBJECTIVES LEARNING
Be able to identify the relationship Be
between the externally applied load, and the internally generated shear force and bending moment force
PR
CE & ME 221 Course Syllabus; Dr. Baladi
Michigan State University
Department of Civil and Environmental Engineering
CE 221 Statics (3 credits) Fall 2014
Prerequisites
The prerequisite courses for CE 221 are PHY 183 and MTH 234 or concurrently or LBS 220 o
SECTION NUMBER _
Michigan State University
Department of Civil and Environmental Engineering
CE 221 Statics (3 credits)
Spring 2015
Sample Test 2
Maximum time is 50 minutes
Note: - This is a closed book and notes test. You are
prohibited from using formul
FORCE SYSTEM RESULTANTS RESULTANTS
Reduction of a Simply Distributed Load Reduction
LEARNING OBJECTIVES LEARNING
Be able to find an equivalent force for a Be simply distributed load simply
PRE-REQUISITE KNOWLEDGE PRE-REQUISITE
Units of measurement Units
FORCE SYSTEM RESULTANTS RESULTANTS
Equivalent System Equivalent
LEARNING OBJECTIVES LEARNING
Be able to find an equivalent force-couple Be
system for a system of forces and couples system
PRE-REQUISITE KNOWLEDGE PRE-REQUISITE
Units of measurement Trigon
Force Vectors Force
Dot Product
LEARNING OBJECTIVES LEARNING
Be able to determine an angle between Be
two vectors. two Be able to determine the projection of a Be vector along a specified line. vector
PRE-REQUISITE KNOWLEDGE PRE-REQUISITE
Units of measu
FORCE VECTORS FORCE
Position and Force Vectors Position Directed Along a Line Directed
LEARNING OBJECTIVES LEARNING
Be able to represent a position Be
vector in Cartesian coordinate form, from given geometry. form, Be able to represent a force vector Be
FORCE VECTORS FORCE
Cartesian Vectors Cartesian (3-Dimensional Vectors) (3-Dimensional
LEARNING OBJECTIVES LEARNING
Be able to resolve each force into its Be rectangular components Fx, Fy and Fz. rectangular Be able to represent the components of force B
FORCE VECTORS FORCE
LEARNING OBJECTIVES LEARNING
Be able to resolve each force into its Be
rectangular components Fx and Fy. rectangular Be able to represent the components of force Be in terms of the Cartesian unit vectors i and j. in Be able to determi
Force Vectors Force
Scalars and Vectors
LEARNING OBJECTIVES LEARNING
Be able to differentiate between Scalar Be
and Vector quantities. and Be able to perform vector operations. Be able to resolve forces into their Be respective components. respective
PRE
Units of Measurement Units
LEARNING OBJECTIVES LEARNING Be able to identify the basic quantities. Be Be able to differentiate between the SI and
FPS systems of unit. FPS Be Be able to convert quantities from one unit system to another. system Be able to d
NEWTONS LAWS NEWTONS
NEWTONS FIRST LAW OF MOTION NEWTONS
An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
NEWTONS SECIND LAW OF
MATRIX DEFINITION
A matrix is defined as a rectangular array matrix of quantities arranged in rows and columns. of
a a . a a 12 13 1n 11 a 21 a 22 a 23 . a 2n a a a . a [ A] = 31 32 33 3n . . . . . a a . a a m2 m3 mn m1 Aij is the quantity A of the ith ro