Question

A 10m long prestressing bed is used to cast beams of 2.3 m each. A schematic representation of the bed is given in the following figure. The continuous prestressing reinforced is pulled at the end 'Y' of the bed through a distance of 20 mm to introduce the required 'prestress' before the concrete is cast. After the concrete has hardened, the prestressing reinforcement is cut at points A,B,C,D and E

Assume that the prestress is introduced without eccentricity, what is the loss in prestress on account of elastic deformation of concrete.Assume $E_s=200000N/m{m}^2,E_c=20000N/m{m}^2,$ Area of prestressing reinforcement is 500 mm${}^2$, size of beam = 200 mm (b) x 400 mm (h)

Answer 1

Elongation in prestressing cable = 20 mm
Strain in prestressing cable
$=\frac{20}{10000}=2\times {10}^{-3}$
Stress in prestressing cable
$=2\times {10}^{-3}\times 2\times {10}^5$
$=400N/m{m}^2$
Prestressing force $=400\times 500$
= 200 kN
Loss in prestress on account of elastic deformation $=m{f}_c$ ....(i)

M = modular ratio
$=\frac{E_s}{E_c}=\frac{200000}{20000}=10$
$f_c=$ stress in concrete at the level of steel
$=\frac{P}{A}=\frac{200\times {10}^3}{200\times 400}$
$=2.5N/m{m}^2$
From (i)
Elastic deformation loss $=10\times 2.5$
$=25N/m{m}^2$