Question

) A 1200 mm deep by 750 mm wide post-tensioned simply supported beam is shown below. The beam spans 12.0 m and is subject to a superimposed dead load of 50 kN/m and a live load of 35 kN/m. Both the superimposed dead load and live load are applied after transfer (after stressing has taken place). The tendon is located at the mid-height of the beam at each end, and its centreline sits 50 mm from the base at midspan. The concrete strength at transfer is 22 MPa, and at maturity is 40 MPa. Assume E_c = 32800 MPa, γ_c = 24 kN/m³ and ignore any prestress losses.

q= If P_i = 1750 kN and all the load has been applied, determine the percentage of the total dead load balanced

Answer 1

Solution:- the values given in the question are as follows:

width of beam(B)=750 mm

depth of beam(d)=1200 mm

length of beam(L)=12 m

dead load(D.L)=50 KN/m

live load(L.L)=35 KN/m

eccentricity at mid span of beam(e)=50 mm

stress in concrete(c)=22 MPa

maturity stress()=40 MPa

young's modulus of elasticity(Ec)=32800 MPa

unit weight of concrete()=24 KN/m^3

q=? , if applied prestressing force(Pi)=1750 KN

let the resisting force developed in tendon due to poststressing force is q, shown in figure.

bending moment at every section of tendon is zero, because the post-stressing force is balanced by resisting force(q) developed in tendon.

so bending moment at mid span of tendon is also zero

-Pi*e+q*(L/2)*(L/4)=0

Pi*e=q*(L^2)/8

q=(8*Pi*e)/L^2 , [Eq-1]

values put in equation-(1) and find the value of q

q={8*1750*(50*10^-3)}/12^2 , [where, e=50mm or 50*10^-3 m]

q=4.8611 kN/m

where, q=resisting force developed in tendon

percentage balanced by q of total dead load

superimposed dead load=50 kN/m and live load=35 kN/m

percentage balanced by q of total dead load=(4.8611/50)*100

percentage balanced by q of total dead load=9.722 %

percentage balanced by q=9.722 % of total load

[Ans]