Slope At Right End Of Simply Supported Beam Carrying UVL With Maximum Intensity At Right End Calculator

Formula Used:

\[ \theta = \frac{q \cdot l^3}{45 \cdot E \cdot I} \]

Uniformly Varying Load (q):

N/m

Length of Beam (l):

Elasticity Modulus of Concrete (E):

Area Moment of Inertia (I):

m⁴

Slope of Beam (θ):

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1. What is the Slope at Right End of Simply Supported Beam carrying UVL?

The slope at the right end of a simply supported beam carrying uniformly varying load with maximum intensity at the right end represents the angle of deflection at that specific support point. This calculation is essential in structural engineering for assessing beam behavior under non-uniform loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta = \frac{q \cdot l^3}{45 \cdot E \cdot I} \]

Where:

\( q \) — Uniformly varying load (N/m)
\( l \) — Length of beam (m)
\( E \) — Elasticity modulus of concrete (Pa)
\( I \) — Area moment of inertia (m⁴)

Explanation: The formula calculates the slope at the right end of a simply supported beam subjected to uniformly varying load with maximum intensity at the right end, considering the beam's material properties and geometric characteristics.

3. Importance of Slope Calculation

Details: Accurate slope calculation is crucial for structural analysis, ensuring beam deflections remain within acceptable limits, and verifying that the structure meets design requirements and safety standards.

4. Using the Calculator

Tips: Enter uniformly varying load in N/m, length in meters, elasticity modulus in Pascals, and area moment of inertia in m⁴. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a uniformly varying load?
A: A uniformly varying load is a distributed load whose magnitude changes linearly along the length of the beam, with maximum intensity at one end.

Q2: Why is the slope at the right end specifically calculated?
A: For beams with maximum load intensity at the right end, the maximum slope typically occurs at this support, making it a critical point for structural analysis.

Q3: What are typical values for elasticity modulus of concrete?
A: Elasticity modulus of concrete typically ranges from 20-40 GPa (20,000,000,000-40,000,000,000 Pa) depending on concrete strength and composition.

Q4: How does area moment of inertia affect the slope?
A: Higher area moment of inertia values result in smaller slopes and deflections, as the beam becomes more resistant to bending.

Q5: Are there limitations to this formula?
A: This formula applies specifically to simply supported beams with uniformly varying load maximum at the right end. Different support conditions or loading patterns require different formulas.