Number of Plates given Maximum Bending Stress Developed in Plates Calculator

✖Point load at center of spring is an equivalent load applied to a single point.ⓘ Point Load at Center of Spring [w]			+10% -10%
✖Span of spring is basically the expanded length of spring.ⓘ Span of Spring [l]			+10% -10%
✖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.ⓘ Maximum Bending Stress in Plates [σ]			+10% -10%
✖Width of Full Size Bearing Plate is the smaller dimension of plate.ⓘ Width of Full Size Bearing Plate [B]			+10% -10%
✖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.ⓘ Thickness of Plate [t_p]			+10% -10%

✖Number of Plates is the count of plates in the leaf spring.ⓘ Number of Plates given Maximum Bending Stress Developed in Plates [n]

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Formula

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Number of Plates given Maximum Bending Stress Developed in Plates

Formula

n = \frac{3 \cdot w \cdot l}{2 \cdot σ \cdot B \cdot {t p}^{2}}

Example

933.7798 = \frac{3 \cdot 251 kN \cdot 6 mm}{2 \cdot 15 MPa \cdot 112 mm \cdot {1.2 mm}^{2}}

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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*t_p^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*t_p^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 00.020 seconds)

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< Torsion of Leaf Spring Calculators

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

Moment of Inertia of each Leaf Spring Plate

Go Moment of Inertia = (Width of Full Size Bearing Plate*Thickness of Plate^3)/12

Total Resisting Moment by n Plates given Bending Moment on each Plate

Go Total Resisting Moments = Number of Plates*Bending Moment in 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*t_p^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 (t_p) 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*t_p^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 (t_p). 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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