Change In Length Of Tapered Bar Calculator

Formula Used:

\[ \Delta L = \frac{F_a \cdot l}{t \cdot E \cdot (L_{Right} - L_{Left})} \cdot \ln\left(\frac{L_{Right}}{L_{Left}}\right) \div 1000000 \]

Applied Force (Fa):

Length of Tapered Bar (l):

Thickness (t):

Young's Modulus (E):

Length of Tapered Bar on Right (LRight):

Length of Tapered Bar on Left (LLeft):

Change in Length of Tapered Bar (ΔL):

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1. What is the Change in Length of Tapered Bar Formula?

The Change in Length of Tapered Bar formula calculates the deformation (ΔL) of a tapered bar when subjected to an applied force. It considers the bar's geometry, material properties, and the applied load to determine the elongation or compression.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Delta L = \frac{F_a \cdot l}{t \cdot E \cdot (L_{Right} - L_{Left})} \cdot \ln\left(\frac{L_{Right}}{L_{Left}}\right) \div 1000000 \]

Where:

\( \Delta L \) — Change in length of tapered bar (m)
\( F_a \) — Applied force (N)
\( l \) — Length of tapered bar (m)
\( t \) — Thickness (m)
\( E \) — Young's modulus (Pa)
\( L_{Right} \) — Length of tapered bar on right side (m)
\( L_{Left} \) — Length of tapered bar on left side (m)

Explanation: The formula accounts for the tapered geometry of the bar and uses natural logarithm to calculate the deformation under applied force.

3. Importance of Change in Length Calculation

Details: Accurate calculation of deformation in tapered bars is crucial for structural design, mechanical engineering applications, and ensuring structural integrity under load.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, Newtons for force, Pascals for Young's modulus). Ensure all values are positive and LRight ≠ LLeft.

5. Frequently Asked Questions (FAQ)

Q1: Why is the natural logarithm used in this formula?
A: The natural logarithm accounts for the tapered geometry and the varying cross-sectional area along the length of the bar.

Q2: What are typical values for Young's modulus?
A: Young's modulus varies by material: steel ≈ 200 GPa, aluminum ≈ 70 GPa, concrete ≈ 30 GPa, rubber ≈ 0.01-0.1 GPa.

Q3: When is this formula applicable?
A: This formula applies to linearly elastic materials with tapered geometry under axial loading within the elastic limit.

Q4: What if LRight equals LLeft?
A: If LRight equals LLeft, the bar is not tapered and a different formula for uniform bars should be used.

Q5: How does thickness affect the deformation?
A: Increased thickness reduces deformation as it increases the cross-sectional area and stiffness of the bar.