Sag of Parabola given Uniform Load Calculator

✖Uniform Load is a load that is distributed or spread across the whole region of an element such as a beam or slab.ⓘ Uniform Load [w_b]			+10% -10%
✖Span Length is the end to end distance between any beam or slab.ⓘ Span Length [L]			+10% -10%
✖Prestressing Force is the force internally applied to the prestressed concrete section.ⓘ Prestressing Force [F]			+10% -10%

✖Sag Length of Cable is the length measured at Midway between Supports is vertical sag at midpoint of cable.ⓘ Sag of Parabola given Uniform Load [L_s]

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Formula

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Sag of Parabola given Uniform Load

Formula

`"L"_{"s"} = "w"_{"b"}*"L"^2/(8*"F")`

Example

`"5m"="0.64kN/m"*("5m")^2/(8*"400kN")`

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Download General Principles of Prestressed Concrete Formulas PDF

Sag of Parabola given Uniform Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sag Length of Cable = Uniform Load*Span Length^2/(8*Prestressing Force)
L_s = w_b*L^2/(8*F)
This formula uses 4 Variables

Variables Used

Sag Length of Cable - (Measured in Meter) - Sag Length of Cable is the length measured at Midway between Supports is vertical sag at midpoint of cable.
Uniform Load - (Measured in Newton per Meter) - Uniform Load is a load that is distributed or spread across the whole region of an element such as a beam or slab.
Span Length - (Measured in Meter) - Span Length is the end to end distance between any beam or slab.
Prestressing Force - (Measured in Kilonewton) - Prestressing Force is the force internally applied to the prestressed concrete section.

STEP 1: Convert Input(s) to Base Unit

Uniform Load: 0.64 Kilonewton per Meter --> 640 Newton per Meter (Check conversion here)
Span Length: 5 Meter --> 5 Meter No Conversion Required
Prestressing Force: 400 Kilonewton --> 400 Kilonewton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_s = w_b*L^2/(8*F) --> 640*5^2/(8*400)

Evaluating ... ...

L_s = 5

STEP 3: Convert Result to Output's Unit

5 Meter --> No Conversion Required

FINAL ANSWER

5 Meter <-- Sag Length of Cable

(Calculation completed in 00.007 seconds)

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< 12 General Principles of Prestressed Concrete Calculators

Resulting Stress due to Moment and Prestress and Eccentric Strands

Go Compressive Stress in Prestress = Prestressing Force/Area of Beam Section+(External Moment*Distance from Centroidal Axis/Moment of Inertia of Section)+(Prestressing Force*Distance from Centroidal Geometric Axis*Distance from Centroidal Axis/Moment of Inertia of Section)

Resulting Stress due to Moment and Prestressing Force

Go Compressive Stress in Prestress = Prestressing Force/Area of Beam Section+(Bending Moment in Prestress*Distance from Centroidal Axis/Moment of Inertia of Section)

Stress due to Prestress Moment

Go Bending Stress in Section = Prestressing Force*Distance from Centroidal Geometric Axis*Distance from Centroidal Axis/Moment of Inertia of Section

Compressive Stress due to External Moment

Go Bending Stress in Section = Bending Moment in Prestress*(Distance from Centroidal Axis/Moment of Inertia of Section)

Length of Span given Uniform Load

Go Span Length = sqrt(8*Sag Length of Cable*Prestressing Force/Uniform Load)

External Moment with Known Compressive Stress

Go External Moment = Bending Stress in Section*Moment of Inertia of Section/Distance from Centroidal Axis

Prestressing Force given Uniform Load

Go Prestressing Force = Uniform Load*Span Length^2/(8*Sag Length of Cable)

Sag of Parabola given Uniform Load

Go Sag Length of Cable = Uniform Load*Span Length^2/(8*Prestressing Force)

Upward Uniform Load using Load Balancing Method

Go Uniform Load = 8*Prestressing Force*Sag Length of Cable/Span Length^2

Cross Sectional Area given Compressive Stress

Go Area of Beam Section = Prestressing Force/Compressive Stress in Prestress

Uniform Compressive Stress due to Prestress

Go Compressive Stress in Prestress = Prestressing Force/Area of Beam Section

Prestressing Force given Compressive Stress

Go Prestressing Force = Area of Beam Section*Compressive Stress in Prestress

Sag of Parabola given Uniform Load Formula

Sag Length of Cable = Uniform Load*Span Length^2/(8*Prestressing Force)
L_s = w_b*L^2/(8*F)

What is Unbonded Post Tensioning?

Unbonded post-tensioning differs from bonded post-tensioning by allowing the tendons permanent freedom of longitudinal movement relative to the concrete. This is most commonly achieved by encasing each individual tendon element within a plastic sheathing filled with a corrosion-inhibiting grease, usually lithium based. Anchorages at each end of the tendon transfer the tensioning force to the concrete, and are required to reliably perform this role for the life of the structure.

How to Calculate Sag of Parabola given Uniform Load?

Sag of Parabola given Uniform Load calculator uses Sag Length of Cable = Uniform Load*Span Length^2/(8*Prestressing Force) to calculate the Sag Length of Cable, The Sag of Parabola given Uniform Load is defined as vertical deflection caused in steel due to only end supports in beam or considered member. Sag Length of Cable is denoted by L_s symbol.

How to calculate Sag of Parabola given Uniform Load using this online calculator? To use this online calculator for Sag of Parabola given Uniform Load, enter Uniform Load (w_b), Span Length (L) & Prestressing Force (F) and hit the calculate button. Here is how the Sag of Parabola given Uniform Load calculation can be explained with given input values -> 5 = 640*5^2/(8*400000).

FAQ

What is Sag of Parabola given Uniform Load?

The Sag of Parabola given Uniform Load is defined as vertical deflection caused in steel due to only end supports in beam or considered member and is represented as L_s = w_b*L^2/(8*F) or Sag Length of Cable = Uniform Load*Span Length^2/(8*Prestressing Force). Uniform Load is a load that is distributed or spread across the whole region of an element such as a beam or slab, Span Length is the end to end distance between any beam or slab & Prestressing Force is the force internally applied to the prestressed concrete section.

How to calculate Sag of Parabola given Uniform Load?

The Sag of Parabola given Uniform Load is defined as vertical deflection caused in steel due to only end supports in beam or considered member is calculated using Sag Length of Cable = Uniform Load*Span Length^2/(8*Prestressing Force). To calculate Sag of Parabola given Uniform Load, you need Uniform Load (w_b), Span Length (L) & Prestressing Force (F). With our tool, you need to enter the respective value for Uniform Load, Span Length & Prestressing Force 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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