SEMINARNITC| CE4092

A UNIFIED APPROACH FOR SHEAR DESIGN OF PRESTRESSED

CONCRETE

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SHEAR STRENGTH

STRENGTH TO RESIST SHEAR

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MODES OF SHEAR FAILURE IN PRESTRESSED CONCRETE BEAM

Web-Shear crackingFlexure-Shear cracking

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Web-Shear strength (Vco):According to IS:1343 (2012) : 0According to ACI 318 (2005) : (0.29

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Flexure-Shear strength (Vcr):According to IS:1343 (2012) : According to ACI 318 (2005)

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EFFECTIVE SHEAR AREA:

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MOHR’S CIRCLE FOR AN ELEMENT TO FIND PRINCIPLE STRESSES

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Equation of Mohr’s Circle

At critical case where tensile strength of concrete reaches its limiting value, evaluating for

The flexural strength σ, along the depth is calculated and substituted in above equation to get

If at section is greater than crack initiation in compression zone takes place and indicated as flexure shear crack

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COMPARISON WITH TEST RESULTS

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SIMPLIFIED METHOD USING A COEFFICIENT K

Above method is an iterative methodInstead an average shear strength of flexure shear is consideredcoefficients of defined as KAverage shear strength of rectangular beam can be defined as

where is the distance of neutral axis from topmost fiber of the cracked section.

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VALUES OF K PLOTTED AGAINST INITIAL PRESTRESSING (PO)

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is a variable and is the ratio of Mo and Mcr

However value of zero to is found satisfactory with many test results.

Therefore

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Above equation holds good for rectangular sectionsCannot be applied directly for Flanged sectionsTests on T beams are carried out to find flange contribution for shearThen b is changed to beff , beff= bw+tf .

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Example Question: (Question is in such a way that Vcr is less than Vco)A post tensioned of 400 mm wide and 550 mm deep.

Factored shear is 150kN, Factored bending moment is 375 kN-m, Effective prestress is 700 kN, fck is 40N/mm2

Area of prestressing steel is 700mm2.Using IS method of analysis:

Substituting values in equation , flexure shear strength is 132.17 kN Using the method described:

finding neutral axis of cracked section we get 121.53 mm substituting this value in , flexure- shear strength of 129.126 kN.

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COMPARISON & CONCLUSIONS:Code considers calculating both Vcr and Vco over the length of the

beam and taking minimum of either.Which means both types of shear cracks can occur even at places

with moment less than cracking moment.However the method described above considers flexure shear

cracks to occur only at places where flexure cracks occur.At sections with moment greater than cracking moment the lower

of flexure-shear and web-shear controlsAt other sections shear cracks are controlled by web shear cracks.

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COMPARISON & CONCLUSIONS

Following the methods that are discussed so far, following equation can be used to compute flexure- shear strength of both Prestressed and non Prestressed concrete members

Wherever the applied moment is greater than the cracking moment, Vcr can be calculated at each section along the depth of section, also to simplify for calculating minimum shear strength section having maximum bending moment can be considered.

APPENDICES:

1) - Tensile strength of concrete

2) - Compressive stress at centroidal axis due to prestressing

3) - Vertical component of prestress

4) - Characteristic strength of concrete

5) - Effective Prestress

6) Mo –Moment required to produce zero stress in concrete at the level of steel

7) Mu –Ultimate bending moment at the section considered due to applied loads18

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