Statics - Equilibrium | Additional Documents & Tests for Civil Engineering (CE) PDF Download

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EQUILIBRIUM 
• Equilibrium is the state of a body in which all its constituent particles are 
at rest or moving uniformly along a straight line relative to an inertial 
reference  
• The study of bodies in equilibrium is called Statics 
• For equilibrium, there must be no force (or equivalent action of no force) 
acting on the body 
• Free body diagram: 
• Diagram showing body under consideration for solving problems in 
statics 
• Obtained by isolating a body from its surrounding and showing all 
forces acting on it 
• Forces acting on a body depends upon support conditions or 
surroundings 
• Internal forces like axial forces, bending moment and shear force 
comes into play when sections or parts of a body is considered 
 
Support Conditions 
 
CONDITIONS FOR EQUILIBRIUM 
• Necessary conditions for a rigid body to be in equilibrium are that resultant 
of force F
R
 and resultant couple moment C
R 
for any point be a zero vector, 
i.e., F
R
=0, C
R
=0, where F
R
 is the sum of forces moved to a common point, 
and C
R
 is the sum of couple moments and moments of all original forces 
about the common point 
Page 2


EQUILIBRIUM 
• Equilibrium is the state of a body in which all its constituent particles are 
at rest or moving uniformly along a straight line relative to an inertial 
reference  
• The study of bodies in equilibrium is called Statics 
• For equilibrium, there must be no force (or equivalent action of no force) 
acting on the body 
• Free body diagram: 
• Diagram showing body under consideration for solving problems in 
statics 
• Obtained by isolating a body from its surrounding and showing all 
forces acting on it 
• Forces acting on a body depends upon support conditions or 
surroundings 
• Internal forces like axial forces, bending moment and shear force 
comes into play when sections or parts of a body is considered 
 
Support Conditions 
 
CONDITIONS FOR EQUILIBRIUM 
• Necessary conditions for a rigid body to be in equilibrium are that resultant 
of force F
R
 and resultant couple moment C
R 
for any point be a zero vector, 
i.e., F
R
=0, C
R
=0, where F
R
 is the sum of forces moved to a common point, 
and C
R
 is the sum of couple moments and moments of all original forces 
about the common point 
• The two independent vector equations of equilibrium for any free body are 
? ?? ?? = ?? ?? ,    ? (?? ?? × ?? ?? )
?? +? ?? ?? = ?? ?? 
where, d
i
 is the displacement vector from common point to any point on 
the line of action of F
i
. These equations are. 
• The six independent scalar equations of equilibrium are: 
? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? 
? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? 
• No more than six unknown quantities in the general case can be solved by 
methods of statics for a single free body 
• For concurrent system of forces, simplest resultant is a single force at the 
point of concurrency. For equilibrium, the requirement is that this force is 
zero, i.e. ? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? , which are the three 
independent equations of equilibrium 
• For coplanar force system, say in xy plane, simplest resultant will be a force 
or a couple in xy plane. For equilibrium, condition is ? (?? ?? )
?? = ?? ?? , 
? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? . These are the three scalar equations of 
equilibrium 
• For parallel forces in space, say, forces being parallel to z-axis, simplest 
resultant is either a force (parallel to z-axis) or a couple moment (in xy 
plane). The three independent scalar equations of equilibrium for this case 
are: ? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? , ? (?? ?? )
?? = ?? ?? . 
• Two-point equivalent loadings – For a body where there is only two points 
of loading (two-force members), to be in equilibrium, the forces must be 
equal and opposite and must have lines of action that are collinear 
• Three force theorem – System of three forces in equilibrium must be 
coplanar and either be concurrent or be parallel 
• When three concurrent coplanar forces are 
in equilibrium, then the forces can be 
represented as a force polygon, which is a 
triangle. Then, by sine rule: 
?? ?? ?????? ?? = 
?? ?? ?????? ?? = 
?? ?? ?????? ??