A post tensioned prestressed concrete beam is having a cross-section of 300 × 300. The area of end block is 100 × 100 mm. Instead of 100 × 100 mm end block, 150 mm × 150 mm end block is provided. What will be the reduction in bursting forces? Let the load in tendons be Po

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MPSC AE CE Mains 2018 Official (Paper 1)

Option 4 : 0.05Po

CT 1: Engineering Mathematics

1077

10 Questions
10 Marks
12 Mins

__Concept:__

**Bursting tensile forces:**

- In
**post-tensioned prestressed concrete (PSC)**beams with mechanical anchorages, the prestressing**force is applied through tendons**and load concentration occurs at the anchorages. - On the basis of the St Venant principle, uniformly distributed stress occurs at the concrete section far away from the anchorage.
**Closer to the anchorage, however, the distribution of stress in the concrete is more complex.** - The
**dispersion of the high local stress**under the anchorage causes**transverse tensile stress,**which may crack the concrete. Accordingly, these transverse tensile stresses referred to as**bursting stresses**have to be determined to arrange proper reinforcements.

**According to IS:1343 (1980):**

The **bursting tensile force**, Fbst existing in an individual square end block loaded by symmetrically placed square anchorage or bearing plate, may be derived from the **equation below**

\(\frac{{{F_{bst}}}}{{{P_0}}} = 0.32 - 0.3\frac{{{y_{p0}}}}{{{y_0}}}\)

Where F_{bst} = Bursting tensile force, P_{0} = Load in tendons, y_{p0} = Width of concrete section, y_{0} = Width of end block

**Calculation:**

**Given:**

y_{0} = 300 mm, y_{01} = 100 mm, y_{02} = 150 mm

\(\frac{{{F_{bst1}}}}{{{P_0}}} = 0.32 - 0.3\frac{{{y_{p01}}}}{{{y_0}}}\)

\(\frac{{{F_{bst1}}}}{{{P_0}}} = 0.32 - 0.3 × \frac{{100}}{{300}}\) = 0.22

**F _{bst1} = P_{0}× 0.22 ** -----------(1)

\(\frac{{{F_{bst2}}}}{{{P_0}}} = 0.32 - 0.3 × \frac{{150}}{{300}}\) = 0.17

**F _{bst2} = 0.17×P_{0} **------------(2)

**Reduction in bursting tensile force = P **= F_{bst2 }- F_{bst1}

= 0.22× P_{0 }- 0.17×P_{0}

**= 0.05×P _{0}**

∴ The reduction in bursting forces is **0.05P _{0}**