Question

 A concrete beam is post-tensioned by a cable carrying initial stress of 1000 N / mm², the slip at jacking end was observed to be 5 mm, modulus of steel is 210 kN / mm² and span of beam is 30 m; what is % of loss of stress due to anchorage?

1. 3.5%
2. 2.5%
3. 1.5%
4. 4.0%

Answer 1

Correct Answer - Option 1 : 3.5%

Concept:

Post-Tensioned:

Post-tensioned concrete is a type of prestressed concrete where the concrete is strengthened via an arrangement of reinforcement held in tension. steel cables, called Post-tensioned tendons. a tendon is generally made of wires, strands, or bars. Wires and strands can be tensioned in groups, whereas bars are tensioned one at a time.

\({\rm{Loss\;of\;stress\;}} = {\rm{Strain\;due\;to\;anchorage}} × {\rm{Modulus\;of\;Elasticity\;}}\)

\({\rm{Strain\;due\;to\;anchorage}} = {\rm{\;}}\frac{{{\rm{Anchorage\;slip}}}}{{{\rm{length\;of\;beam}}}}\)

\({\rm{Percentage\;loss\;in\;pre}} {\rm{stress}} = \frac{{{\rm{loss\;in\;pre}} {\rm{stress}}}}{{{\rm{initial\;pre}}{\rm{stress}}}} × 100\)

Calculation:

Given,

Anchorage slip = 5 mm; Beam length = 30 m; Modulus of Elasticity of steel = 2.1 × 105 N/mm2,

initial pre-stress = 1000 N/mm2

\({\rm{Strain\;due\;to\;anchorage}} = {\rm{\;}}\frac{5}{{30 × 1000}} = {\rm{\;}}{1.67\ × 10^{ - 4}}\)

Loss of stress = 1.67 × 10-4 × 2.1 × 105 = 35 MPa

\({\rm{Percentage\;loss\;in\;pre}} - {\rm{stress}} = {\rm{\;}}\frac{{35}}{{1000}} × 100\)

∴ Loss in pre-stress = 3.5%