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UDL given Maximum Reactions at Supports Formula

GoUniformly distributed Load given Horizontal Component of Cable Tension for UDL Formula

GoUDL given Vertical Reaction at Supports Formula

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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. Check FAQs

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

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

UDL given Maximum Reactions at Supports Example

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

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

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

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

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

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

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UDL given Maximum Reactions at Supports Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

q = \frac{93750N}{(\frac{15m}{2}) \cdot \sqrt{1 + (\frac{{15m}^{2}}{16 \cdot {5m}^{2}})}}

Next Step Prepare to Evaluate

∴

q = \frac{93750}{(\frac{15}{2}) \cdot \sqrt{1 + (\frac{15^{2}}{16 \cdot 5^{2}})}}

Next Step Evaluate

∴

q = 10000N/m

LAST Step Convert to Output's Unit

∴

q = 10kN/m

UDL given Maximum Reactions at Supports Formula Elements

Variables

Functions

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

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

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 to find Uniformly Distributed Load

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 UDL given Vertical Reaction at Supports

q = 2 \cdot \frac{V R}{L span}

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 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}

Go Vertical Reaction at Supports

V R = q \cdot \frac{L span}{2}

How to Evaluate UDL given Maximum Reactions at Supports?

UDL given Maximum Reactions at Supports evaluator uses Uniformly Distributed Load = Maximum Value of Tension/((Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2)))) to evaluate the Uniformly Distributed Load, The UDL given Maximum Reactions at Supports formula is defined as the total load acting on the cable per meter horizontal length of cable. Uniformly Distributed Load is denoted by q symbol.

How to evaluate UDL given Maximum Reactions at Supports using this online evaluator? To use this online evaluator for UDL given Maximum Reactions at Supports, enter Maximum Value of Tension (T_max), Cable Span (L_span) & Sag of Cable at Midway between Supports (f) and hit the calculate button.

FAQs on UDL given Maximum Reactions at Supports

What is the formula to find UDL given Maximum Reactions at Supports?

The formula of UDL given Maximum Reactions at Supports is expressed as Uniformly Distributed Load = Maximum Value of Tension/((Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2)))). Here is an example- 0.01 = 93750/((15/2)*sqrt(1+((15^2)/(16*5^2)))).

How to calculate UDL given Maximum Reactions at Supports?

With Maximum Value of Tension (T_max), Cable Span (L_span) & Sag of Cable at Midway between Supports (f) we can find UDL given Maximum Reactions at Supports using the formula - Uniformly Distributed Load = Maximum Value of Tension/((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).

What are the other ways to Calculate Uniformly Distributed Load?

Here are the different ways to Calculate Uniformly Distributed Load-

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

Can the UDL given Maximum Reactions at Supports be negative?

Yes, the UDL given Maximum Reactions at Supports, measured in Surface Tension can be negative.

Which unit is used to measure UDL given Maximum Reactions at Supports?

UDL given Maximum Reactions at Supports is usually measured using the Kilonewton per Meter[kN/m] for Surface Tension. Newton per Meter[kN/m], Millinewton per Meter[kN/m], Gram-Force per Centimeter[kN/m] are the few other units in which UDL given Maximum Reactions at Supports can be measured.

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UDL given Maximum Reactions at Supports Formula

​GoUniformly distributed Load given Horizontal Component of Cable Tension for UDL Formula

​GoUDL given Vertical Reaction at Supports Formula

UDL given Maximum Reactions at Supports Example

UDL given Maximum Reactions at Supports Solution

UDL given Maximum Reactions at Supports Formula Elements

Other Formulas to find Uniformly Distributed Load

Other formulas in Supports at Same Level category

How to Evaluate UDL given Maximum Reactions at Supports?

FAQs on UDL given Maximum Reactions at Supports

Variable Name

GoUniformly distributed Load given Horizontal Component of Cable Tension for UDL Formula

GoUDL given Vertical Reaction at Supports Formula