Question

Calculate the minimum prestressing force required for Beam 1 knowing that the beam has a cross sectional area of 200 × 500 mm and an allowable stress of 0.3 N/mm2 . External Load applied in Tons/m is 150

Answer 1

Given Data -

Width (b) = 200 mm
Depth (d) = 500 mm
External Load (we) = 150 T/m (1500 kN/m)
Total load (w) = Self Weight + we

Step 1: Considering the length (L) of the beam to be 0.5 meters and the prestressing to be concentric, the basic working principle for the problem ca be determined.

The loads acting on the beam can be realised as shown below:

  

The Mid-Span moment in this case is given by,   

Step 2: The resultant and Individual forces diagrams can be represented as shown :

  

Step 3: Calculations
The relation between Prestressing stress and stress generated due to external load and self weight is
  

Here, A = 200 x 500 = 0.1 m2
W = 1500 + (0.2 x 0.5 x 25) = 1525 kN/m
L = 0.5 m
Zb = 0.00833 m3

Therefore, Prestressing stress (P/A) = 5721 kN/m2

Prestressing Force required = 5721 x 0.2 x 0.5 kN = 5721 kN .