Maximum Deflection Of Simply Supported Beam Carrying Couple Moment At Right End Calculator

Formula Used:

\[ \delta = \frac{M_c \cdot l^2}{15.5884 \cdot E \cdot I} \]

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):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The maximum deflection of a simply supported beam carrying a couple moment at the right end refers to the maximum displacement experienced by the beam under the applied moment. This calculation is essential in structural engineering to ensure beams meet design requirements and safety standards.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta = \frac{M_c \cdot l^2}{15.5884 \cdot E \cdot I} \]

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: This 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 structural design to ensure beams can withstand applied loads without excessive deformation that could compromise structural integrity or serviceability.

4. Using the Calculator

Tips: Enter moment of couple in N·m, length in meters, elasticity modulus in Pascals, 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 two supports at its ends, allowing rotation but preventing vertical movement at the support points.

Q2: What is a couple moment?
A: A couple moment consists of two equal and opposite forces that are separated by a perpendicular distance, creating a pure moment without resultant force.

Q3: Why is the constant 15.5884 used in the formula?
A: This constant is derived from the integration of the bending moment equation for this specific loading condition and support configuration.

Q4: What factors affect beam deflection?
A: Beam deflection is influenced by the applied loads, beam length, material properties (elastic modulus), and cross-sectional properties (moment of inertia).

Q5: How can deflection be reduced in beam design?
A: Deflection can be reduced by using stiffer materials (higher E), increasing the moment of inertia (larger cross-sections), shortening the span length, or adding additional supports.