This document discusses couples and their properties. A couple is formed by two equal but opposite parallel forces separated by a perpendicular distance. The moment of a couple is the product of one of the forces and the perpendicular distance between them. Couples cause rotation without translation. They contribute to the resulting moment but not force in a system. In prestressed concrete beams, the compressive force in concrete and tensile force in steel form an internal resisting couple. The lever arm of this couple increases to resist external moments up to the point of failure.

1. Ahsanullah University of
Science And Technology
Prepared By
Course no: CE 416
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2. Objectives :
Introduction of Couple
 Understanding the Properties of a Couple.
 Analyzing the Characteristics of a Couple.
 What a couple does
 Internal resisting couple

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3. Definition of a
couple :
When two parallel f orces
are equal but opposite in sense
and are not collinear they f orm
a couple.
The moment of a
couple is the product of one of
the f orces and the perpendicular
distance between the lines of
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4. F
d
F
θ
F
d
θ
F
The above f igure indicates a
counterclockwise couple where the
moment of the couple
M= F* d
here ,
F = Force acting on the body.
d = Moment arm of the couple.
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5. Properties of a couple :
o
Equal magnitude and opposite in direction .
o
Act along parallel lines of action .
o
Separated by a perpendicular distance .
o
The orientation of the plane of the couple in
relation to the body upon which it acts .
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6. Characteristics of
couples :
•
A couple has the same moment about all points
on a body.
F
F
F
F
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7. 
A couple may be transformed into
another couple that produces the same
external effect.

A force may be resolved into a force
and a couple where a single force and a
couple cannot balance one another.
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8. F
A
d
F
B
A
F
A
MA = F x d
F
d
B
B
Force Couple Equivalent
F
The above shows how a force can be
replaced by a force-couple equivalent.
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9. 
The resultant of several couples in the same plane
or parallel planes has a magnitude equal to the sum
of several couple moments
200 lb
150 lb
A
B
C
100 lb
D
250 lb
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10. What a couple
does?

A couple causes a body to rotate only
without translational motion since the two
forces ‘cancels’ out each other giving zero
resultant.

A couple acting in a system of forces
will only contribute to the resulting moment
but not to the resulting force.
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11. Internal resisting couple in a pre stressed
concrete beam :
Fig: Internal resisting
couple with arm a
In the figure a pre
stressed concrete
beam is shown
where
Steel is supplying
the tensile force T
and the concrete is
supplying the
compressive force
C. Whre C and T
together form a
couple,with arm a .
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12. 
The couple C-T is formed in order to
resist the external moment.
For a pre stressed concrete beam
Resistance to external moment is gained by
lengthening of the lever arm between the
couple C-T.

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13. 
In a prestressed concreted beam section
under working load, as the external bending moment
increases ,the magnitude of C and T reamins practically
constant while the lever arm ‘a’ lengthens almost
proportionately.
Fig: Variable a in a prestressed –concrete beam
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14. 
When a section of a prestressed
beam is subjected to a crack under working
load the stress in steel increases and
reaching to its ultimate strength the lever
arm of the internal couple cannot be
increased anymore which results in the
point of failure.
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15. Nominal & Ultimate
resisting moment : Maximum value of the
internal resisting couple is
termed as nominal moment
strength.which must resists
the bending moment applied
by the external loads.
 From the internal resisting couple the ultimate
resisting moment can also be computed which represents
the very last point of the beam failure. From the above
figure for C-T force couple, the ultimate resisting
moment according to ACI code,
Mu = φ [Apsfps (d - a/2)]
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16. The End ..........
Special Thanks To:
Mr.Galib sir
Lecturer at
AUST
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