Engineering Mechanics: StaticsAndrew Zulu

GO3; 061-2072514

Module 0: Introduction to Statics

AMC 110S

S ta tic s D yn am ics

R ig id B od ies(Th in g s th a t d o n o t ch an g e sh ap e)

D eform ab le B od ies(Th in g s th a t d o ch an g e sh ap e)

In com p ress ib le C om p ress ib le

F lu id s

M ech an ics

Mechanics - historical development

Galileo Galilei (1564-1647) Isaac Newton (1643-1727) Albert Einstein (1879-1955)

Werner Heinsenberg (1901-1976) Max Planck (1858-1947).

Mechanics/Basic Concepts

• (Oldest) Physical science – effects of forces on bodies

Vectors

• Free vector – action not confined to free line in space e.g. moment vector

• Sliding vector – unique line of action but no confined point of application e.g. force vector (principle of transmissibility of force)

• Fixed vector – unique point of application e.g. non-rigid body force

Vectors (null)

Vectors (parallelogram &triangle/polygon rule)

Vectors (negative)

Vectors (rectangular/orthogonal components)

Vectors (3-D)

Example 1

Example 2

Given: Three concurrent forces acting on a tent post.

Find: The magnitude and angle of the resultant force.

F1 = {0 i + 300 j } N F2 = {– 450 cos (45°) i + 450 sin (45°) j } N

= {– 318.2 i + 318.2 j } NF3 = { (3/5) 600 i + (4/5) 600 j } N

= { 360 i + 480 j } N

Example 2 (cont’d)

• Summing up all the i and j components respectively, we get,

• FR = { (0 – 318.2 + 360) i + (300 + 318.2 + 480) j } N

• = { 41.80 i + 1098 j } N

Using magnitude and direction:

FR = ((41.80)2 + (1098)2)1/2 = 1099 N

= tan-1(1098/41.80) = 87.8° x

y

FR

Vectors – dot (scalar) product

• The dot product of vectors A and B is defined as A•B = A B cos .

• The angle is the smallest angle between the two vectors and is always in a range of 0º to 180º.

, i • j = 0 i • i = 1

A • B = (Ax i + Ay j + Az k) • (Bx i + By j + Bz k) = Ax Bx + AyBy + AzBz

= cos-1 [(A • B)/(A B)], where 0º 180º

Example 3

• r = i + 2 j 2 k => r = (12 + 22 + 22)1/2 = 3

• F = 6 i + 9 j + 3 k => F = (62 + 92 + 32)1/2 = 11.22

• F • r = ( 6)(1) + (9)(2) + (3)(2) = 18

= cos-1{(F • r)/(F r)}

= cos-1 {18 / (11.22 * 3)} = 57.7°

Vectors – cross (vector) product

C = A B = A B sin uC

i j = k

i i = 0

Example 4

• r = 3 j + 1.5 k• F = 6 i + 3 j + 10• r x F = | I j k |• | 0 3 1.5 | • | -6 3 10 |

= [{3(10) – 1.5(3)} i – {0(10) – 1.5(– 6)} j + {0(3) – 3(– 6)} k]

= 25.5 i + 9 j + 18 k