Variation of Eccentricity of Tendon B Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
EB(x) = eB1+(4*ΔeB*x/L)*(1-(x/L))
This formula uses 5 Variables
Variables Used
Eccentricity Variation of Tendon B - (Measured in Meter) - Eccentricity Variation of Tendon B is the value for eccentricity at distance x from left jacking side of considered prestress section.
Eccentricity at End for B - (Measured in Meter) - Eccentricity at End for B is the distance by which the tendons at end is placed from the CG of section.
Change in Eccentricity B - (Measured in Meter) - Change in Eccentricity B refers the eccentricity of tendon B when the eccentricity at both ends and centre is considered.
Distance from Left End - (Measured in Meter) - Distance from Left End is the distance considered from the left jacking end on a prestressed member.
Length of Beam in Prestress - (Measured in Meter) - Length of Beam in Prestress is the center to center distance between the supports or the effective length of the beam.
STEP 1: Convert Input(s) to Base Unit
Eccentricity at End for B: 10.03 Millimeter --> 0.01003 Meter (Check conversion here)
Change in Eccentricity B: 20 Millimeter --> 0.02 Meter (Check conversion here)
Distance from Left End: 10.1 Millimeter --> 0.0101 Meter (Check conversion here)
Length of Beam in Prestress: 10.2 Meter --> 10.2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
EB(x) = eB1+(4*ΔeB*x/L)*(1-(x/L)) --> 0.01003+(4*0.02*0.0101/10.2)*(1-(0.0101/10.2))
Evaluating ... ...
EB(x) = 0.0101091372472126
STEP 3: Convert Result to Output's Unit
0.0101091372472126 Meter -->10.1091372472126 Millimeter (Check conversion here)
FINAL ANSWER
10.1091372472126 10.10914 Millimeter <-- Eccentricity Variation of Tendon B
(Calculation completed in 00.004 seconds)

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NSS College of Engineering (NSSCE), Palakkad
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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

Variation of Eccentricity of Tendon B Formula

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))
EB(x) = eB1+(4*ΔeB*x/L)*(1-(x/L))

what are the applications of Post Tensioned system?

(i)Post tensioning is ideally suited for medium to long span in situ nook & hence it is more economical.

(ii) It allows the use of curved and shopped off cables which helps the designer to vary the prestress distribution at will from section to section so as to counter the external loads more efficiently.

(iii)It is invariably used is strengthening concrete dams.

(iv) It is ideally suited for the work involving stage prestressing

How to Calculate Variation of Eccentricity of Tendon B?

Variation of Eccentricity of Tendon B calculator uses 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)) to calculate the Eccentricity Variation of Tendon B, The Variation of Eccentricity of Tendon B is defined as the eccentricity at a distance x from left jacking end if parabolic tendons are used for prestressing beam. Eccentricity Variation of Tendon B is denoted by EB(x) symbol.

How to calculate Variation of Eccentricity of Tendon B using this online calculator? To use this online calculator for Variation of Eccentricity of Tendon B, enter Eccentricity at End for B (eB1), Change in Eccentricity B (ΔeB), Distance from Left End (x) & Length of Beam in Prestress (L) and hit the calculate button. Here is how the Variation of Eccentricity of Tendon B calculation can be explained with given input values -> 10109.14 = 0.01003+(4*0.02*0.0101/10.2)*(1-(0.0101/10.2)).

FAQ

What is Variation of Eccentricity of Tendon B?
The Variation of Eccentricity of Tendon B is defined as the eccentricity at a distance x from left jacking end if parabolic tendons are used for prestressing beam and is represented as EB(x) = eB1+(4*ΔeB*x/L)*(1-(x/L)) or 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)). Eccentricity at End for B is the distance by which the tendons at end is placed from the CG of section, Change in Eccentricity B refers the eccentricity of tendon B when the eccentricity at both ends and centre is considered, Distance from Left End is the distance considered from the left jacking end on a prestressed member & Length of Beam in Prestress is the center to center distance between the supports or the effective length of the beam.
How to calculate Variation of Eccentricity of Tendon B?
The Variation of Eccentricity of Tendon B is defined as the eccentricity at a distance x from left jacking end if parabolic tendons are used for prestressing beam is calculated using 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)). To calculate Variation of Eccentricity of Tendon B, you need Eccentricity at End for B (eB1), Change in Eccentricity B (ΔeB), Distance from Left End (x) & Length of Beam in Prestress (L). With our tool, you need to enter the respective value for Eccentricity at End for B, Change in Eccentricity B, Distance from Left End & Length of Beam in Prestress 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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