CE 201 - Statics

Lecture 2

Contents

Vector Operations– Multiplication and Division of Vectors– Addition of Vectors– Subtraction of vectors– Resolution of a Vector

Vector Addition of Forces Analysis of Problems

Vector Operations

Multiplication and Division of a Vector by a Scalar Vector A Scalar a A a = aA Magnitude of aA Direction of A if a is positive (+) Direction of –A (opposite) if a is negative (-)

A

-A

1.5 A

Vector Addition

Vectors are added according to the parallelogram law The resultant R is the diagonal of the parallelogram

If two vectors are co-linear (both have the same line of action), they are added algebraically

A

B

A

B

R = A + BA

B

R = A + B BA

R = A + B

A B

R = A + B

Vector Subtraction

The resultant is the difference between vectors A and B

A

B -B

AR

R

A-B

Resolution of a Vector

If lines of action are known, the resultant R can be resolved into two components acting along those lines (i.e. a and b).

a

b

A

B R

Vector addition of Forces

Force!Is it vector OR scalar? Why?

The two common problems encountered in STATICS are:1. Finding the RESULTANT (by knowing the COMPONENTS).

OR2. Resolving a FORCE into its COMPONENTS (by applying the

parallelogram law).

If more than two forces are to be added!!Apply the same law more than once depending on the number of forces.

3 Forces

F1

F2

F3

R1=F1+F2

R2=R1+F3

Four Forces

F1

F2

F3

R1=F1+F2

R2=R1+F3

F4R3=R2+F4

Analysis of Problems

Two procedures to be followed: Parallelogram law Trigonometry sine and/or cosine laws may be used

Sine Law

A/sin (a) = B/sin (b) = C/sin (c)

a

A B

bC

c

Cosine Law

C = A2+B2-2ABcos (c)

a

A B

bC

c

Examples

2.1 2.2 2.3 2.4 Problem 2-8 Problem 2-25