Average Stress for Parabolic Tendons Solution

STEP 0: Pre-Calculation Summary
Formula Used
Average Stress = Stress at End+2/3*(Stress at Midspan-Stress at End)
fc,avg = fc1+2/3*(fc2-fc1)
This formula uses 3 Variables
Variables Used
Average Stress - (Measured in Pascal) - Average Stress is the stress when parabolic tendons are used in prestressed section caused due to stress in concrete at end and mid span.
Stress at End - (Measured in Pascal) - Stress at End is the stress in concrete at the ends of the member.
Stress at Midspan - (Measured in Pascal) - Stress at Midspan refers to the stress in concrete due to tenons in the midspan of the member.
STEP 1: Convert Input(s) to Base Unit
Stress at End: 10.006 Megapascal --> 10006000 Pascal (Check conversion here)
Stress at Midspan: 10.3 Megapascal --> 10300000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
fc,avg = fc1+2/3*(fc2-fc1) --> 10006000+2/3*(10300000-10006000)
Evaluating ... ...
fc,avg = 10202000
STEP 3: Convert Result to Output's Unit
10202000 Pascal -->10.202 Megapascal (Check conversion here)
FINAL ANSWER
10.202 Megapascal <-- Average Stress
(Calculation completed in 00.020 seconds)

Credits

Created by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
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Verified by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
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13 Post-Tensioned Members Calculators

Variation of Eccentricity on Tendon A
Go Eccentricity Variation of Tendon A = Eccentricity at End for A+(4*Change in Eccentricity at A*Distance from Left End/Length of Beam in Prestress)*(1-(Distance from Left End/Length of Beam in Prestress))
Variation of Eccentricity of Tendon B
Go Eccentricity Variation of Tendon B = Eccentricity at End for B+(4*Change in Eccentricity B*Distance from Left End/Length of Beam in Prestress)*(1-(Distance from Left End/Length of Beam in Prestress))
Prestress Drop given Stress in concrete at Same Level due to Prestressing Force
Go Prestress Drop = Modulus of Elasticity of Steel Reinforcement*Stress in Concrete Section/Modulus of Elasticity Concrete
Prestress Drop given Strain due to Bending and Compression in Two Parabolic Tendons
Go Prestress Drop = Modulus of Elasticity of Steel Reinforcement*(Strain due to Compression+Strain due to Bending)
Area of Concrete Section given Prestress Drop
Go Concrete Occupied Area = Modular Ratio for Elastic Shortening*Prestress Force/(Prestress Drop)
Average Stress for Parabolic Tendons
Go Average Stress = Stress at End+2/3*(Stress at Midspan-Stress at End)
Change in Eccentricity of Tendon A due to Parabolic Shape
Go Change in Eccentricity at A = Eccentricity at Midspan for A-Eccentricity at End for A
Stress in Concrete given Prestress Drop
Go Stress in Concrete Section = Prestress Drop/Modular Ratio for Elastic Shortening
Prestress Drop given Modular Ratio
Go Prestress Drop = Modular Ratio for Elastic Shortening*Stress in Concrete Section
Component of Strain at Level of First Tendon due to Bending
Go Strain due to Bending = Change in Length Dimension/Length of Beam in Prestress
Change in Eccentricity of Tendon B due to Parabolic Shape
Go Change in Eccentricity B = Eccentricity at Midspan B-Eccentricity at End for B
Prestress Drop
Go Prestress Drop = Modulus of Elasticity of Steel Reinforcement*Change in Strain
Prestress Drop when Two parabolic Tendons are Incorporated
Go Prestress Drop = Modulus of Elasticity of Steel Reinforcement*Concrete Strain

Average Stress for Parabolic Tendons Formula

Average Stress = Stress at End+2/3*(Stress at Midspan-Stress at End)
fc,avg = fc1+2/3*(fc2-fc1)

How the Loss of Stress in Bending Members are found?

The calculation of loss for tendons stretched sequentially, is similar to post-tensioned
axial members. For curved profiles, the eccentricity of the CGS and hence, the stress in
concrete at the level of CGS vary along the length. An average stress in concrete can
be considered.

How to Calculate Average Stress for Parabolic Tendons?

Average Stress for Parabolic Tendons calculator uses Average Stress = Stress at End+2/3*(Stress at Midspan-Stress at End) to calculate the Average Stress, The Average Stress for Parabolic Tendons is defined as the equation for finding the average stress in the concrete when parabolic tendons are used in the member. The stresses are considered at both ends and midspan of the member. Average Stress is denoted by fc,avg symbol.

How to calculate Average Stress for Parabolic Tendons using this online calculator? To use this online calculator for Average Stress for Parabolic Tendons, enter Stress at End (fc1) & Stress at Midspan (fc2) and hit the calculate button. Here is how the Average Stress for Parabolic Tendons calculation can be explained with given input values -> 1E-5 = 10006000+2/3*(10300000-10006000).

FAQ

What is Average Stress for Parabolic Tendons?
The Average Stress for Parabolic Tendons is defined as the equation for finding the average stress in the concrete when parabolic tendons are used in the member. The stresses are considered at both ends and midspan of the member and is represented as fc,avg = fc1+2/3*(fc2-fc1) or Average Stress = Stress at End+2/3*(Stress at Midspan-Stress at End). Stress at End is the stress in concrete at the ends of the member & Stress at Midspan refers to the stress in concrete due to tenons in the midspan of the member.
How to calculate Average Stress for Parabolic Tendons?
The Average Stress for Parabolic Tendons is defined as the equation for finding the average stress in the concrete when parabolic tendons are used in the member. The stresses are considered at both ends and midspan of the member is calculated using Average Stress = Stress at End+2/3*(Stress at Midspan-Stress at End). To calculate Average Stress for Parabolic Tendons, you need Stress at End (fc1) & Stress at Midspan (fc2). With our tool, you need to enter the respective value for Stress at End & Stress at Midspan and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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