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Basic Assumptions
1. Concrete is a homogeneous elastic material.
2. Within the range of working stress, both concrete & steel behave elastically, notwithstanding the small amount of creep, which occurs in both the materials under sustained loading.
3. A plane section before bending is assumed to remain plane even after bending, which implies a linear strain distribution across the depth of the member.
Following are the three concepts of analysis
Tendon with Parabolic ProfileLet l be the span of the beam and h be the dip of the cable.
The cable will exert an upward udl = w_{C }/ m on the beam, but the cable will be subjected to a downward udl of w_{C} per unit run.
Let V and H are vertical and horizontal components of P.
V = w_{c}l / 2
The cable is an absolutely flexible member, therefore BM at every section of cable is zero. Hence BM at the centre of the cable is
Since dip of the cable is very small, we can make an approximation
cosα = 1 and Pcosα = P
Now consider the beam, it is subjected to
(i) External load w per unit length
(ii) Upward udl transmitted by the cable = w_{C} per unit length.
Net UDL = w – w_{C}
Net BM at the centre
Extreme stresses = P / A ± Net BM / Z
Losses of Prestress
The steel wires of a prestressed concrete member do not retain all the preliminary prestress. A certain amount of loss of prestress always takes place.
Losses may be classified as follows:
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