Statics Final

of 13 Mr. Mohammed Elkably

Statics Final revision

Rules

=

= ac + bd

such that: = (a, b) , = (c, d)

= 2 + 2

Note: = 0 if, = 0 , = 0 or

The algebraic projection of in the direction of =

x = (A B sin )

x = , x = , x =

x = - , x = - , x = -

x = 0 , x = 0 , x = 0

(a + b ) x ( c + d ) = (ad bc)

Area of triangle =

2

Unit vector perpendicular to each of and =

( + ) = +



The moment of acts at A about B is:

MB = x = BA . F . sin

Length of perpendicular ( arm) =

1) If line of action passing through the point A, then : MA = 0

2) The algebraic component of force in the direction of =

3) If the force bisects , then: MA = - MB

4) If the force is parallel to then: MA = MB

Same Direction:

R = F1 + F2 ( Magnitude)

F1 . AB = F2 . BC ( Line of action)

A B C

F1 F2

R

A B C

F2

F1

R

Opposite Direction:

R = F2 F1 ( Magnitude)

F2 . AB = F! . AC ( Line of action)

Two couples are equivalent, then M1 = M2 , (Same sign)

Two couples are equilibrium, then M1 = -M2 (diff sign)



If: F1, F2, and F3 are is same way round:

Then, 1

=

2

=

3

= m

The set of forces is equivalent to a couple

M= 2 m.A

Area of triangle = 1

2 base x height

= 1

2 a b sin C

= . . .

such that: s = 1

2 (a + b+ c)

A

B C

F1

F2

F3



Definitions

1) Condition of equilibrium of a group of coplanar forces.

( the sum of forces in the direction of x-axis = the sum of forces in the

direction of y-axis = the sum of moments of forces about any point = 0)

2) Angle of friction ()

( the angle included between the resultant reaction and the perpendicular

reaction when the body is about to slide) ( tan = )

3) Coefficient of friction () (The ratio between the limiting friction force and the normal reaction)

4) Limiting friction force:

(The force of friction on the body when it is about to move and its equal to )

5) The couple:

( A couple consists of two forces equal in magnitude, parallel in opposite

directions, there is a distance apart between them)

6) Mention the equations of the equilibrium of a rigid body under the

action of a set of collinear forces.

( the sum of forces in the direction of x-axis = the sum of forces in the

direction of y-axis = the sum of moments of forces about any point = 0)



A) Complete

1)

2)

3)

4)

5)

6)

7)



8)

9)

10) If the friction force F < the limiting friction force , then the body ..

11) A couple is consists of two forces..



B) Inclined rod

1)

2)

3)

4)

5)



C) Horizontal rod

1)

2)

3)

4)



D) Lamina

1)

2)

3)

E) Vectors

1)

2)

3)



F) Planes

1)

2)

3)

4)

5)



6)

7)



G) Shapes

1)

2)

3)

4)

5)

6)

7)



8)

9)

10)

11)

Statics Final

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