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

Formula Used:

\[ \theta = \frac{7 \cdot q \cdot l^3}{360 \cdot E \cdot I} \]

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 Left End of Simply Supported Beam Carrying UVL with Maximum Intensity at Right End?

The slope at the left end of a simply supported beam carrying a uniformly varying load with maximum intensity at the right end represents the angle of rotation at that support. This parameter is crucial in structural analysis to understand beam deflection behavior under non-uniform loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta = \frac{7 \cdot q \cdot l^3}{360 \cdot E \cdot I} \]

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: This formula calculates the slope at the left end of a simply supported beam subjected to a uniformly varying load that reaches its maximum intensity at the right end.

3. Importance of Slope Calculation

Details: Calculating beam slope is essential for structural design to ensure that deflections and rotations remain within acceptable limits for serviceability and safety requirements.

4. Using the Calculator

Tips: Enter the uniformly varying load in N/m, beam length in meters, elasticity modulus in Pa, and area moment of inertia in m⁴. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the elasticity modulus of concrete important?
A: The elasticity modulus represents the stiffness of the concrete material and directly affects how much the beam will deflect under load.

Q3: What is area moment of inertia?
A: Area moment of inertia is a geometric property that measures a beam's resistance to bending based on its cross-sectional shape and size.

Q4: Are there limitations to this formula?
A: This formula applies specifically to simply supported beams with uniformly varying load maximum at the right end and assumes linear elastic material behavior.

Q5: What are typical slope values in beam design?
A: Acceptable slope values depend on the specific application and building codes, but generally small slopes (typically less than 1-2 degrees) are desired for serviceability.