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Maximum Reactions at Supports Formula

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Maximum Value of Tension that occurs at the supports is a sum of both horizontal and vertical force. Check FAQs

T max = (q \cdot \frac{L span}{2}) \cdot \sqrt{1 + (\frac{{L span}^{2}}{16 \cdot f^{2}})}

T_max - Maximum Value of Tension?q - Uniformly Distributed Load?L_span - Cable Span?f - Sag of Cable at Midway between Supports?

Maximum Reactions at Supports Example

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Here is how the Maximum Reactions at Supports equation looks like with Values.

Here is how the Maximum Reactions at Supports equation looks like with Units.

Here is how the Maximum Reactions at Supports equation looks like.

93.75 = (10 \cdot \frac{15}{2}) \cdot \sqrt{1 + (\frac{15^{2}}{16 \cdot 5^{2}})}

93.75kN = (10kN/m \cdot \frac{15m}{2}) \cdot \sqrt{1 + (\frac{{15m}^{2}}{16 \cdot {5m}^{2}})}

93.75 = (10 \cdot \frac{15}{2}) \cdot \sqrt{1 + (\frac{15^{2}}{16 \cdot 5^{2}})}

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Maximum Reactions at Supports Solution

Follow our step by step solution on how to calculate Maximum Reactions at Supports?

FIRST Step Consider the formula

T max = (q \cdot \frac{L span}{2}) \cdot \sqrt{1 + (\frac{{L span}^{2}}{16 \cdot f^{2}})}

Next Step Substitute values of Variables

∴

T max = (10kN/m \cdot \frac{15m}{2}) \cdot \sqrt{1 + (\frac{{15m}^{2}}{16 \cdot {5m}^{2}})}

Next Step Convert Units

∴

T max = (10000N/m \cdot \frac{15m}{2}) \cdot \sqrt{1 + (\frac{{15m}^{2}}{16 \cdot {5m}^{2}})}

Next Step Prepare to Evaluate

∴

T max = (10000 \cdot \frac{15}{2}) \cdot \sqrt{1 + (\frac{15^{2}}{16 \cdot 5^{2}})}

Next Step Evaluate

∴

T max = 93750N

LAST Step Convert to Output's Unit

∴

T max = 93.75kN

Maximum Reactions at Supports Formula Elements

Variables

Functions

Maximum Value of Tension

Maximum Value of Tension that occurs at the supports is a sum of both horizontal and vertical force.

Symbol: T_max

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Maximum Value of Tension

Uniformly Distributed Load

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.

Symbol: q

Measurement: Surface TensionUnit: kN/m

Note: Value can be positive or negative.

Formulas to find Uniformly Distributed Load

Cable Span

Cable Span is total length of cable in horizontal direction.

Symbol: L_span

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cable Span

Sag of Cable at Midway between Supports

Sag of Cable at Midway between Supports is vertical sag at midpoint of cable.

Symbol: f

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Sag of Cable at Midway between Supports

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.

Syntax: sqrt(Number)

Other formulas in Supports at Same Level category

Go Horizontal Component of Cable Tension for UDL

T cable udl = q \cdot \frac{{L span}^{2}}{8 \cdot f}

Go Uniformly distributed Load given Horizontal Component of Cable Tension for UDL

q = \frac{T cable udl \cdot 8 \cdot f}{{(L span)}^{2}}

Go Span Length given Horizontal Component of Cable Tension for UDL

L span = \sqrt{\frac{8 \cdot f \cdot T cable udl}{q}}

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

f = q \cdot \frac{{L span}^{2}}{8 \cdot T cable udl}

How to Evaluate Maximum Reactions at Supports?

Maximum Reactions at Supports evaluator 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 evaluate 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 evaluate Maximum Reactions at Supports using this online evaluator? To use this online evaluator 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.

FAQs on Maximum Reactions at Supports

What is the formula to find Maximum Reactions at Supports?

The formula of Maximum Reactions at Supports is expressed as Maximum Value of Tension = (Uniformly Distributed Load*Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2))). Here is an example- 0.09375 = (10000*15/2)*sqrt(1+((15^2)/(16*5^2))).

How to calculate Maximum Reactions at Supports?

With Uniformly Distributed Load (q), Cable Span (L_span) & Sag of Cable at Midway between Supports (f) we can find Maximum Reactions at Supports using the formula - Maximum Value of Tension = (Uniformly Distributed Load*Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2))). This formula also uses Square Root (sqrt) function(s).

Can the Maximum Reactions at Supports be negative?

No, the Maximum Reactions at Supports, measured in Force cannot be negative.

Which unit is used to measure Maximum Reactions at Supports?

Maximum Reactions at Supports is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Maximum Reactions at Supports can be measured.

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Maximum Reactions at Supports Formula

Maximum Reactions at Supports Example

Maximum Reactions at Supports Solution

Maximum Reactions at Supports Formula Elements

Other formulas in Supports at Same Level category

How to Evaluate Maximum Reactions at Supports?

FAQs on Maximum Reactions at Supports

Variable Name