Slope At Right End Of Simply Supported Beam Carrying Couple At Right End Calculator

Formula Used:

\[ \theta = \frac{M_c \cdot l}{3 \cdot E \cdot I} \]

Moment of Couple (Mc):

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 Slope at Right End of Simply Supported Beam?

The slope at the right end of a simply supported beam carrying a couple at the right end represents the angle of rotation of the beam at that specific support point. This calculation is essential in structural engineering for understanding beam deflection behavior.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta = \frac{M_c \cdot l}{3 \cdot E \cdot I} \]

Where:

\( M_c \) — Moment of couple (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 when a couple moment is applied at that end, considering the beam's material properties and geometry.

3. Importance of Slope Calculation

Details: Calculating beam slope is crucial for structural analysis, ensuring that deflections and rotations remain within acceptable limits for safety and serviceability requirements in construction projects.

4. Using the Calculator

Tips: Enter moment of couple in N·m, beam length in meters, elasticity modulus in Pascals, and area moment of inertia in m⁴. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a simply supported beam?
A: A simply supported beam is a structural element that rests on two supports at its ends, allowing rotation but preventing translation at the support points.

Q2: What is the significance of the couple moment?
A: The couple moment represents a pair of equal and opposite forces that create pure bending moment at the beam end, causing rotation without translation.

Q3: How does elasticity modulus affect the slope?
A: Higher elasticity modulus (stiffer material) results in smaller slopes, as the beam resists deformation more effectively.

Q4: What is area moment of inertia?
A: Area moment of inertia is a geometric property that measures a beam's resistance to bending, depending on its cross-sectional shape and dimensions.

Q5: Are there limitations to this formula?
A: This formula applies specifically to simply supported beams with a couple applied at the right end and assumes linear elastic material behavior and small deformations.