1. CE-416
Pre-stressed Concrete Lab Sessional
Presented By:
ABU SYED MD. TARIN
Id No:10.01.03.020
Course teachers:
Munshi Galib Muktadir
Sabreena Nasrin
Department Of Civil Engineering
Ahsanullah University of Science &
technology
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2.  Stiffness method is an efficient way to solve complex
determinant or indeterminant structures . It will
introduced that is a modern method for structural
analysis. which is a powerful engineering method and
has been applied in numerous engineering fields such
as solid mechanics and fluid mechanics. it is also
called the displacement method.
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3. 
A statically indeterminate structure that the reaction
and internal forces cannot be analyzed by the application of
the equation of static alone . The indeterminacy of the
structure may be either external ,internal or both . The space
structute is externally indeterminate if the number of the
reaction components is more than six.
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4.  Identify degree of kinematic indeterminacy (doki)
 Apply restraints and make it kinematically determinate
 Apply loads on the fully restraint structure and calculate
forces.
 Apply unknown displacements to the structure one at a
time keeping all other displacements zero and calculate
forces corresponding to each dof.
 Write the equilibrium equations. solve the equation in
matrix form and obtain the value of unknown
displacements.
 Calculate other reactions.(by super position)
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5. 
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The number of possible directions that displacements or forces
at a node can exist in is termed a degree of freedom (dof ). Some
examples are:
Plane truss: has 2 degrees of freedom at each node:
translation/forces in the x and y directions.
Beams: have 2 degrees of freedom per node: vertical
displacement/forces and rotation/moment.
Plane Frame: has 3 degrees of freedom at each node: the
translations/forces similar to a plane truss and in addition, the
rotation or moment at the joint.
Space Truss: a truss in three dimensions has 3 degrees of
freedom: translation or forces along each axis in space.
Space Frame: has 6 degrees of freedom at each node:
translation/forces along each axis, and rotation/moments about
each axis.
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6.  For frame ,doki=8*3-(3+2)=19
 For beam, doki=4*2-(2+1)=5
 For truss, doki=6*2-(2+2+1)=7
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7.  For the case of symmetry & antysymmetry, use of modified
stiffness makes the problem easier. Previously, it was
derived that stiffness factor =3EI/L when the far end is
hinged. This is also modified stiffness.
 Modified Stiffness K’=2EI/L=K/2 (For symmetry).
K’=6EI/l=3k/2 (For Antisymmetry).
K’= 3EI/L (When Far End Hinged)
Determination Of Stiffness Factor
 Case(i)When the far end is hinged: K=4EI/L.
 Case(ii)When the far end is fixed : MAB=3EI/L.
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8. Direct Stiffness Method for Truss Analysis
 The members are straight, slender, and prismatic. The crosssectional dimensions are small in comparison to the member
lengths.
 The joints are assumed to be frictionless pins (or internal
hinges).
 The loads are applied only at the joints in the form of
concentrated forces.
Direct Stiffness Method for Frame Analysis
 The members are slender and prismatic. They can be straight or
curved, vertical, horizontal, or inclined.
 The joints can be assumed to be rigid connection, frictionless
pins (or internal hinges), or typical connections.
 The loads can be concentrated forces or moments that act at
joints or on the frame members, or distributed forces acting on
the members.
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10. Solution
 In the first step identify the degrees of freedom of the
frame .The given frame has three degrees of freedom
(i) Two rotations as indicated by U1 and U2
 (ii) One horizontal displacement of joint B and C as
indicated by U3
 In the next step make all the displacements equal to
zero by fixing joints B and C as shown in Fig.23.5c. On
this kinematically determinate structure apply all the
external loads and calculate reactions corresponding
to unknown joint displacements .
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