Deflection At Any Point On Simply Supported Carrying Couple Moment At Right End Calculator

Formula Used:

\[ \delta = \left( \frac{M_c \cdot l \cdot x}{6 \cdot E \cdot I} \right) \cdot \left(1 - \frac{x^2}{l^2} \right) \]

Moment of Couple (M_c):

N·m

Length of Beam (l):

Distance x from Support (x):

Elasticity Modulus of Concrete (E):

Area Moment of Inertia (I):

m⁴

Deflection of Beam (δ):

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1. What is the Deflection Formula?

The formula calculates the deflection at any point on a simply supported beam carrying a couple moment at the right end. It considers the moment of couple, beam length, distance from support, elasticity modulus, and moment of inertia.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta = \left( \frac{M_c \cdot l \cdot x}{6 \cdot E \cdot I} \right) \cdot \left(1 - \frac{x^2}{l^2} \right) \]

Where:

\( \delta \) — Deflection of Beam (m)
\( M_c \) — Moment of Couple (N·m)
\( l \) — Length of Beam (m)
\( x \) — Distance x from Support (m)
\( E \) — Elasticity Modulus of Concrete (Pa)
\( I \) — Area Moment of Inertia (m⁴)

Explanation: The formula accounts for the beam's material properties, geometry, and loading conditions to determine deflection at any point.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring beams meet serviceability requirements and don't exceed allowable deflection limits.

4. Using the Calculator

Tips: Enter all values in appropriate units. Moment of couple, length, distance, elasticity modulus, and moment of inertia must be positive values.

5. Frequently Asked Questions (FAQ)

Q1: What is a simply supported beam?
A: A beam supported at both ends, free to rotate at supports without vertical movement restraints.

Q2: What is moment of couple?
A: A system of two equal and opposite parallel forces that produce rotation without translation.

Q3: What are typical deflection limits?
A: Deflection limits vary by application but are typically L/240 to L/360 for live loads and L/180 to L/240 for total loads.

Q4: How does elasticity modulus affect deflection?
A: Higher elasticity modulus results in less deflection as the material is stiffer and resists deformation better.

Q5: What is area moment of inertia?
A: A geometric property that measures a beam's resistance to bending based on its cross-sectional shape and size.