10.01.03.075 Equilibrium and equation of equilibrium:2D

1. WELCOME TO MY
PRESENTATION

2. AHSANULLAH UNIVERSITY
OF
SCIENCE AND TECHNOLOGY
PRE-STRESSED CONCRETE
SESSIONAL

3. PRESENTED BY
MUNSHI MD. RASEL
ID: 10.01.03.075
SECTION B
4th YEAR AND 2nd SEMESTER
DEPARTMENT OF CIVIL ENGINEERING

4. PRESENTATION TOPIC
EQUILIBRIUM AND EQUATION OF
EQUILIBRIUM:2D

5. Equilibrium
A body is said to be in
equilibrium if it is at
rest or moving with
uniform velocity.

6. Newton’s First Law of Motion: If the
resultant force on a particle is zero, the
particle will remain at rest or will
continue at constant speed in a straight
line.

7. Factors that affect equilibrium


Area of the base:
the bigger the area
of the base, the
more the stable the
object is
Weight: the heavier
the object is, the
more stable it is

8. Types of Equilibrium
 Static
Equilibrium
 Dynamic Equilibrium

9. Static Equilibrium
If some forces are
acting on a body
horizontally or
vertically, and the
body remains it states
of rest is called Static
Equilibrium. Example:
A book lying on a
table.

10. Dynamic Equilibrium
If some forces are
acting on a body
horizontally or
vertically, and the
body remains it states
of motion is called
Dynamic Equilibrium.
Example: A train is
moving with uniform
velocity.

11. Equations of equilibrium
Consider an object
moving along the xaxis. If no net force is
applied to the object
along the x-axis, it will
continue to move
along the x-axis at a
constant velocity with
no acceleration. We
can extend this to the
y- and z- axes.

12. In static systems, where motion does not
occur, the sum of the forces in all
directions must always equal zero
(otherwise, it's a dynamics problem). This
concept can be represented
mathematically with the following
equations:

13. ∑Fx=0
∑Fy=0
∑Fz=0

14.  The
concept also applies to rotational
motion.
 If the resultant moment about an axis is
zero, the object will have no rotational
acceleration about the axis. Again, we can
extend this to moments about the y-axis
and the z-axis. This is represented
mathematically with the following.

15. ∑Mx=0
∑My=0
∑Mz=0

16. ∑F=0 : The algebraic
sum of all the
horizontal or vertical
forces acting on a
body which is in
equilibrium must
equal zero.

17. ∑M=0: The algebraic
sum of the moments
of all the forces acting
on a body which is in
equilibrium, about any
point in the plane of
those forces, must
equal zero.

18. There are six equations expressing the
equilibrium of a rigid body in 3 dimensions.
∑Fx=0
∑Fy=0
∑Fz=0
∑Mx=0
∑My=0 ∑Mz=0

19. In two dimensions one direction of force
and two directions of moments can be
ignored. When forces exist only in the x
and y directions, there cannot be a
moment in any direction except z. The
equations of concern when forces only
exist in the x and y directions are shown
below:

20. ∑Fx=0
∑Fy=0
∑Mz=0

21. How to apply equations of
equilibrium?
 First
draw a free body diagram of the
structure or its member.
 If a member is selected, it must be
isolated from its supports and
surroundings.
 All the forces and couple moments must
be shown acting on the member.
 Then apply the equations of equilibrium.

22. y
FBD at A
FD A
Area to be cut
or isolated
FB
A
30˚
x

23. Example
 Find
the reactions at support of the
following beam:

24. Applying eqn of equilibrium:
∑Fx=0;
Ax=0
∑Fy=0;
Ay+By-10-20*4=0
Ay+By=90kn………(1)

25. Considering Z axis passing through A and
taking moment of all the forces about Zaxis (taking clockwise –ve and
anticlockwise +ve)
∑Mz=0; By*10-10*8-20*4*2=0
By=24kn
Putting this value in eqn (1) we get,
Ay=66kn.

26. 2D Equilibrium - Applications
Since the forces involved in supporting the spool lie in a plane, this is
essentially a 2D equilibrium problem. How would you find the forces in
cables AB and AC?

27. 2D Equilibrium -- Applications
2D Equilibrium Applications
For a given force exerted on the boat’s towing pendant, what are
the forces in the bridle cables? What size of cable must you use?
This is again a 2D problem since the forces in cables AB, BC, and
BD all lie in the same plane.

28. Summary
•
In order for an object to be in equilibrium,
there must be no net force on it along any
coordinate, and there must be no net
torque around any axis.
•
2D equations of equilibrium:
∑Fx=0
∑Fy=0
∑Mz=0

29. Thanks for your kind attention
Any Questions?