Maximum Reactions at Supports Calculator

✖Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.ⓘ Uniformly Distributed Load [q]			+10% -10%
✖Cable Span is total length of cable in horizontal direction.ⓘ Cable Span [L_span]			+10% -10%
✖Sag of Cable at Midway between Supports is vertical sag at midpoint of cable.ⓘ Sag of Cable at Midway between Supports [f]			+10% -10%

✖Maximum Value of Tension that occurs at the supports is a sum of both horizontal and vertical force.ⓘ Maximum Reactions at Supports [T_max]

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Maximum Reactions at Supports Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Value of Tension = (Uniformly Distributed Load*Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2)))
T_max = (q*L_span/2)*sqrt(1+((L_span^2)/(16*f^2)))
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Maximum Value of Tension - (Measured in Newton) - Maximum Value of Tension that occurs at the supports is a sum of both horizontal and vertical force.
Uniformly Distributed Load - (Measured in Newton per Meter) - Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.
Cable Span - (Measured in Meter) - Cable Span is total length of cable in horizontal direction.
Sag of Cable at Midway between Supports - (Measured in Meter) - Sag of Cable at Midway between Supports is vertical sag at midpoint of cable.

STEP 1: Convert Input(s) to Base Unit

Uniformly Distributed Load: 10 Kilonewton per Meter --> 10000 Newton per Meter (Check conversion here)
Cable Span: 15 Meter --> 15 Meter No Conversion Required
Sag of Cable at Midway between Supports: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_max = (q*L_span/2)*sqrt(1+((L_span^2)/(16*f^2))) --> (10000*15/2)*sqrt(1+((15^2)/(16*5^2)))

Evaluating ... ...

T_max = 93750

STEP 3: Convert Result to Output's Unit

93750 Newton -->93.75 Kilonewton (Check conversion here)

FINAL ANSWER

93.75 Kilonewton <-- Maximum Value of Tension

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< Supports at Same Level Calculators

Span Length given Horizontal Component of Cable Tension for UDL

LaTeX Go Cable Span = sqrt((8*Sag of Cable at Midway between Supports*Cable Tension for UDL)/Uniformly Distributed Load)

Sag of Cable at Midway between supports given Horizontal Component of Cable Tension for UDL

LaTeX Go Sag of Cable at Midway between Supports = Uniformly Distributed Load*(Cable Span^2)/(8*Cable Tension for UDL)

Uniformly distributed Load given Horizontal Component of Cable Tension for UDL

LaTeX Go Uniformly Distributed Load = (Cable Tension for UDL*8*Sag of Cable at Midway between Supports)/(Cable Span)^2

Horizontal Component of Cable Tension for UDL

LaTeX Go Cable Tension for UDL = Uniformly Distributed Load*(Cable Span^2)/(8*Sag of Cable at Midway between Supports)

Maximum Reactions at Supports Formula

LaTeX Go

Maximum Value of Tension = (Uniformly Distributed Load*Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2)))
T_max = (q*L_span/2)*sqrt(1+((L_span^2)/(16*f^2)))

What is Cable?

Cables are flexible structures that support the applied transverse loads by the tensile resistance developed in its members. Cables are used in suspension bridges, tension leg offshore platforms, transmission lines, and several other engineering applications.

How to Calculate Maximum Reactions at Supports?

Maximum Reactions at Supports calculator uses Maximum Value of Tension = (Uniformly Distributed Load*Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2))) to calculate the Maximum Value of Tension, The Maximum Reactions at Supports formula is defined as the summation of horizontal and vertical force acting at any point in the cable. Maximum Value of Tension is denoted by T_max symbol.

How to calculate Maximum Reactions at Supports using this online calculator? To use this online calculator for Maximum Reactions at Supports, enter Uniformly Distributed Load (q), Cable Span (L_span) & Sag of Cable at Midway between Supports (f) and hit the calculate button. Here is how the Maximum Reactions at Supports calculation can be explained with given input values -> 0.09375 = (10000*15/2)*sqrt(1+((15^2)/(16*5^2))).

FAQ

What is Maximum Reactions at Supports?

The Maximum Reactions at Supports formula is defined as the summation of horizontal and vertical force acting at any point in the cable and is represented as T_max = (q*L_span/2)*sqrt(1+((L_span^2)/(16*f^2))) or Maximum Value of Tension = (Uniformly Distributed Load*Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2))). Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element, Cable Span is total length of cable in horizontal direction & Sag of Cable at Midway between Supports is vertical sag at midpoint of cable.

How to calculate Maximum Reactions at Supports?

The Maximum Reactions at Supports formula is defined as the summation of horizontal and vertical force acting at any point in the cable is calculated using Maximum Value of Tension = (Uniformly Distributed Load*Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2))). To calculate Maximum Reactions at Supports, you need Uniformly Distributed Load (q), Cable Span (L_span) & Sag of Cable at Midway between Supports (f). With our tool, you need to enter the respective value for Uniformly Distributed Load, Cable Span & Sag of Cable at Midway between Supports 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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