UDL given Maximum Reactions at Supports Calculator

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

✖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.ⓘ UDL given Maximum Reactions at Supports [q]

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UDL given Maximum Reactions at Supports Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Maximum Value of Tension: 93.75 Kilonewton --> 93750 Newton (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

q = T_max/((L_span/2)*sqrt(1+((L_span^2)/(16*f^2)))) --> 93750/((15/2)*sqrt(1+((15^2)/(16*5^2))))

Evaluating ... ...

q = 10000

STEP 3: Convert Result to Output's Unit

10000 Newton per Meter -->10 Kilonewton per Meter (Check conversion here)

FINAL ANSWER

10 Kilonewton per Meter <-- Uniformly Distributed Load

(Calculation completed in 00.004 seconds)

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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)

UDL given Maximum Reactions at Supports Formula

LaTeX Go

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

What is Cable Tension?

Cable tension is determined by measuring the amount of force needed to make an offset in the cable between two hardened steel blocks called anvils. A riser or plunger is pressed against the cable to form the offset

How to Calculate UDL given Maximum Reactions at Supports?

UDL given Maximum Reactions at Supports calculator 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 calculate 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 calculate UDL given Maximum Reactions at Supports using this online calculator? To use this online calculator 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. Here is how the UDL given Maximum Reactions at Supports calculation can be explained with given input values -> 0.01 = 93750/((15/2)*sqrt(1+((15^2)/(16*5^2)))).

FAQ

What is UDL given Maximum Reactions at Supports?

The UDL given Maximum Reactions at Supports formula is defined as the total load acting on the cable per meter horizontal length of cable and is represented as q = T_max/((L_span/2)*sqrt(1+((L_span^2)/(16*f^2)))) or Uniformly Distributed Load = Maximum Value of Tension/((Cable Span/2)*sqrt(1+((Cable Span^2)/(16*Sag of Cable at Midway between Supports^2)))). Maximum Value of Tension that occurs at the supports is a sum of both horizontal and vertical force, 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 UDL given Maximum Reactions at Supports?

The UDL given Maximum Reactions at Supports formula is defined as the total load acting on the cable per meter horizontal length of cable is calculated using 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 calculate UDL given Maximum Reactions at Supports, you need Maximum Value of Tension (T_max), Cable Span (L_span) & Sag of Cable at Midway between Supports (f). With our tool, you need to enter the respective value for Maximum Value of Tension, 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.

How many ways are there to calculate Uniformly Distributed Load?

In this formula, Uniformly Distributed Load uses Maximum Value of Tension, Cable Span & Sag of Cable at Midway between Supports. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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