Center Deflection of Simply Supported Beam carrying Couple Moment at Right End Calculator

Formula Used:

\[ \delta = \frac{M_c \cdot l^2}{16 \cdot E \cdot I} \]

Moment of Couple (M_c):

N·m

Length of Beam (l):

Elasticity Modulus of Concrete (E):

Area Moment of Inertia (I):

m⁴

Deflection of Beam (δ):

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1. What is Center Deflection of Simply Supported Beam carrying Couple Moment at Right End?

The center deflection of a simply supported beam carrying a couple moment at the right end refers to the maximum vertical displacement at the midpoint of the beam when subjected to a moment couple applied at one end. This calculation is essential in structural engineering for assessing beam performance under specific loading conditions.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

\[ \delta = \frac{M_c \cdot l^2}{16 \cdot E \cdot I} \]

Where:

\( \delta \) — Deflection of beam (m)
\( M_c \) — 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 maximum deflection at the center of a simply supported beam when a couple moment is applied at the right end, considering the beam's material properties and geometry.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for ensuring structural integrity, preventing excessive deformation, and meeting design specifications in construction and engineering applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: What is moment of couple?
A: Moment of couple is equal to the product of either of the forces and the perpendicular distance between the forces, creating a rotational effect without translation.

Q3: What are typical values for elasticity modulus of concrete?
A: Typical values range from 20-30 GPa (20,000,000,000-30,000,000,000 Pa) for normal strength concrete, depending on the mix design and age.

Q4: How does beam length affect deflection?
A: Deflection increases with the square of the beam length, meaning longer beams will experience significantly more deflection under the same loading conditions.

Q5: What are acceptable deflection limits?
A: Acceptable deflection limits vary by application and building codes, but typically range from L/180 to L/360 of the span length for different structural elements.