Question

A prestressed concrete beam, 200mm wide and 300 mm deep, is prestressed with
wires (area = 320 mm) located at & constant eccentricity of 50 mm and carrying an
initial stress of 1000 N/mm². The span of the beam is 10m. Calculate the
percentage loss of stress in wires if (a) the beam is pre-tensioned and (b) the beam
is post-tensioned, using the following data: Es = 210 kN/mm and Ec = 35 kN/mm²;
relaxation of stress in steel 5 percent of the initial stress, shrinkage of concrete =
300 x 10-6 for pre tensioning and 200 x 10-6 for post tensioning; creep coefficient =
1.6; slip at anchorage 1 mm; frictional coefficient for wave effect = 0.0015 per
m.​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

The answer is ,

The percentage loss of stress in wire due to pre-tensioned  and post-tensioned is 22.33%

Explanation:

Given,

e = 50 mm

Area of cable = 320 mm²

Initial stress = 1000 Mpa

Length of Span (l) = 10m

Prestressing force P = 1000×320 = 320 kN

Es = 210 kN/mm

Ec = kN/mm²

Relaxation of stress in steel 5 percent of initial stress, Shrinkage of concrete for

Pre-tensioning= 300×$10^{-6}$

Post Tensioning = 200×$10^{-6}$

Creep coefficient = 1.6

Frictional coefficient for wave effect = 0.0015/m

Solution:

When beam is pretensioned,

Elastic deformation loss = m $f_{c avg}$

            m = $\frac{E_{s} }{E_{c} }$  

                = $\frac{210}{35}$

                = 6

         $f_{c avg}$ = $\frac{P}{A}$ + $\frac{(Pe) e}{I}$

        $f_{c avg}$ = {(320× 10³)/ (200×300)} + {(320×10³×10⁵)/{(200×300³)/12}}

                 = 7.11 MPa

Elastic Deformation loss = 6×7.11

                                        = 42.667 MPa

Shrinkage loss = $E_{cs}E_{s}$

                     = (300×$10^{-6}$)×210×10³ MPa

                     = 63 MPa

Relaxation loss = $\frac{5}{100}$ × 1000

                         = 50 MPa

Creep loss = mθ$f_{c avg}$

                  = 6 × 1.6 ×7.111

                  = 68.266 MPa

Total loss =223.333 MPa

% in loss = $\frac{223.33}{1000}$× 100

              = 22.3 %

Answer : The percentage loss of stress in wires during the pre tensioned and post tensioned using the following data is 22.3%.

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