Number of Plates given Maximum Bending Stress Developed in Plates Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of Plates = (3*Point Load at Center of Spring*Span of Spring)/(2*Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2)
n = (3*w*l)/(2*σ*B*tp^2)
This formula uses 6 Variables
Variables Used
Number of Plates - Number of Plates is the count of plates in the leaf spring.
Point Load at Center of Spring - (Measured in Newton) - Point load at center of spring is an equivalent load applied to a single point.
Span of Spring - (Measured in Meter) - Span of spring is basically the expanded length of spring.
Maximum Bending Stress in Plates - (Measured in Pascal) - Maximum bending stress in plates is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
Width of Full Size Bearing Plate - (Measured in Meter) - Width of Full Size Bearing Plate is the smaller dimension of plate.
Thickness of Plate - (Measured in Meter) - The thickness of plate is the state or quality of being thick. The measure of the smallest dimension of a solid figure: a board of two-inch thickness.
STEP 1: Convert Input(s) to Base Unit
Point Load at Center of Spring: 251 Kilonewton --> 251000 Newton (Check conversion here)
Span of Spring: 6 Millimeter --> 0.006 Meter (Check conversion here)
Maximum Bending Stress in Plates: 15 Megapascal --> 15000000 Pascal (Check conversion here)
Width of Full Size Bearing Plate: 112 Millimeter --> 0.112 Meter (Check conversion here)
Thickness of Plate: 1.2 Millimeter --> 0.0012 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
n = (3*w*l)/(2*σ*B*tp^2) --> (3*251000*0.006)/(2*15000000*0.112*0.0012^2)
Evaluating ... ...
n = 933.779761904762
STEP 3: Convert Result to Output's Unit
933.779761904762 --> No Conversion Required
FINAL ANSWER
933.779761904762 933.7798 <-- Number of Plates
(Calculation completed in 00.004 seconds)

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17 Torsion of Leaf Spring Calculators

Point Load Acting at Center of Spring given Maximum Bending Stress Developed in Plates
Go Point Load at Center of Spring = (2*Number of Plates*Width of Full Size Bearing Plate*Thickness of Plate^2*Maximum Bending Stress in Plates)/(3*Span of Spring)
Maximum Bending Stress Developed in Plates given Point Load at Center
Go Maximum Bending Stress in Plates = (3*Point Load at Center of Spring*Span of Spring)/(2*Number of Plates*Width of Full Size Bearing Plate*Thickness of Plate^2)
Number of Plates given Maximum Bending Stress Developed in Plates
Go Number of Plates = (3*Point Load at Center of Spring*Span of Spring)/(2*Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2)
Maximum Bending Stress Developed given Central Deflection of Leaf Spring
Go Maximum Bending Stress in Plates = (4*Modulus of Elasticity Leaf Spring*Thickness of Plate*Deflection of Centre of Leaf Spring)/(Span of Spring^2)
Central Deflection of Leaf Spring for given Modulus of Elasticity
Go Deflection of Centre of Leaf Spring = (Maximum Bending Stress in Plates*Span of Spring^2)/(4*Modulus of Elasticity Leaf Spring*Thickness of Plate)
Modulus of Elasticity given Central Deflection of Leaf Spring
Go Modulus of Elasticity Leaf Spring = (Maximum Bending Stress in Plates*Span of Spring^2)/(4*Deflection of Centre of Leaf Spring*Thickness of Plate)
Number of Plates in Leaf Spring given Total Resisting Moment by n Plates
Go Number of Plates = (6*Bending Moment in Spring)/(Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2)
Total Resisting Moment by n Plates
Go Total Resisting Moments = (Number of Plates*Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2)/6
Maximum Bending Stress Developed given Radius of Plate to which they are Bent
Go Maximum Bending Stress in Plates = (Modulus of Elasticity Leaf Spring*Thickness of Plate)/(2*Radius of Plate)
Modulus of Elasticity given Radius of Plate to which they are Bent
Go Modulus of Elasticity Leaf Spring = (2*Maximum Bending Stress in Plates*Radius of Plate)/(Thickness of Plate)
Radius of Plate to which they are Bent
Go Radius of Plate = (Modulus of Elasticity Leaf Spring*Thickness of Plate)/(2*Maximum Bending Stress in Plates)
Point Load at Center of Spring Load given Bending Moment at Center of Leaf Spring
Go Point Load at Center of Spring = (4*Bending Moment in Spring)/(Span of Spring)
Moment of Inertia of each Leaf Spring Plate
Go Moment of Inertia = (Width of Full Size Bearing Plate*Thickness of Plate^3)/12
Radius of Plate to which they are Bent given Central Deflection of Leaf Spring
Go Radius of Plate = (Span of Spring^2)/(8*Deflection of Centre of Leaf Spring)
Central Deflection of Leaf Spring
Go Deflection of Centre of Leaf Spring = (Span of Spring^2)/(8*Radius of Plate)
Total Resisting Moment by n Plates given Bending Moment on each Plate
Go Total Resisting Moments = Number of Plates*Bending Moment in Spring
Load at One End given Bending Moment at Center of Leaf Spring
Go Load at One End = (2*Bending Moment in Spring)/Span of Spring

Number of Plates given Maximum Bending Stress Developed in Plates Formula

Number of Plates = (3*Point Load at Center of Spring*Span of Spring)/(2*Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2)
n = (3*w*l)/(2*σ*B*tp^2)

What is bending stress in beam?

When a beam is subjected to external loads, shear forces and bending moments develop in the beam. The beam itself must develop internal resistance to resist shear forces and bending moments. The stresses caused by the bending moments are called bending stresses.

How to Calculate Number of Plates given Maximum Bending Stress Developed in Plates?

Number of Plates given Maximum Bending Stress Developed in Plates calculator uses Number of Plates = (3*Point Load at Center of Spring*Span of Spring)/(2*Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2) to calculate the Number of Plates, The Number of plates given maximum bending stress developed in plates formula is defined as the count of plates on leaf spring. Number of Plates is denoted by n symbol.

How to calculate Number of Plates given Maximum Bending Stress Developed in Plates using this online calculator? To use this online calculator for Number of Plates given Maximum Bending Stress Developed in Plates, enter Point Load at Center of Spring (w), Span of Spring (l), Maximum Bending Stress in Plates (σ), Width of Full Size Bearing Plate (B) & Thickness of Plate (tp) and hit the calculate button. Here is how the Number of Plates given Maximum Bending Stress Developed in Plates calculation can be explained with given input values -> 109.7668 = (3*251000*0.006)/(2*15000000*0.112*0.0012^2).

FAQ

What is Number of Plates given Maximum Bending Stress Developed in Plates?
The Number of plates given maximum bending stress developed in plates formula is defined as the count of plates on leaf spring and is represented as n = (3*w*l)/(2*σ*B*tp^2) or Number of Plates = (3*Point Load at Center of Spring*Span of Spring)/(2*Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2). Point load at center of spring is an equivalent load applied to a single point, Span of spring is basically the expanded length of spring, Maximum bending stress in plates is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend, Width of Full Size Bearing Plate is the smaller dimension of plate & The thickness of plate is the state or quality of being thick. The measure of the smallest dimension of a solid figure: a board of two-inch thickness.
How to calculate Number of Plates given Maximum Bending Stress Developed in Plates?
The Number of plates given maximum bending stress developed in plates formula is defined as the count of plates on leaf spring is calculated using Number of Plates = (3*Point Load at Center of Spring*Span of Spring)/(2*Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2). To calculate Number of Plates given Maximum Bending Stress Developed in Plates, you need Point Load at Center of Spring (w), Span of Spring (l), Maximum Bending Stress in Plates (σ), Width of Full Size Bearing Plate (B) & Thickness of Plate (tp). With our tool, you need to enter the respective value for Point Load at Center of Spring, Span of Spring, Maximum Bending Stress in Plates, Width of Full Size Bearing Plate & Thickness of Plate 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 Number of Plates?
In this formula, Number of Plates uses Point Load at Center of Spring, Span of Spring, Maximum Bending Stress in Plates, Width of Full Size Bearing Plate & Thickness of Plate. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Number of Plates = (6*Bending Moment in Spring)/(Maximum Bending Stress in Plates*Width of Full Size Bearing Plate*Thickness of Plate^2)
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