Straight Beam Deflection Calculator

Beam Deflection Formula:

\[ \delta = \frac{k_b \cdot T_l \cdot l^3}{E_c \cdot I} + \frac{k_s \cdot T_l \cdot l}{G \cdot A} \]

Beam Loading Constant (k_b):

Total Beam Load (T_l):

Beam Span (l):

Modulus of Elasticity of Concrete (E_c):

MPa

Moment of Inertia (I):

kg·m²

Support Condition Constant (k_s):

Shear Modulus (G):

MPa

Cross-Sectional Area of Beam (A):

m²

Deflection of Beam (δ):

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1. What is Beam Deflection?

Beam deflection is the degree to which a structural element is displaced under a load due to its deformation. It may refer to an angle or a distance and is a critical factor in structural engineering design.

2. How Does the Calculator Work?

The calculator uses the beam deflection formula:

\[ \delta = \frac{k_b \cdot T_l \cdot l^3}{E_c \cdot I} + \frac{k_s \cdot T_l \cdot l}{G \cdot A} \]

Where:

\( \delta \) — Deflection of beam (m)
\( k_b \) — Beam loading constant
\( T_l \) — Total beam load (kN)
\( l \) — Beam span (m)
\( E_c \) — Modulus of elasticity of concrete (MPa)
\( I \) — Moment of inertia (kg·m²)
\( k_s \) — Support condition constant
\( G \) — Shear modulus (MPa)
\( A \) — Cross-sectional area of beam (m²)

Explanation: The formula accounts for both bending and shear deformations in the beam under load.

3. Importance of Beam Deflection Calculation

Details: Accurate deflection calculation is crucial for ensuring structural integrity, preventing excessive deformation, meeting serviceability requirements, and maintaining safety standards in construction projects.

4. Using the Calculator

Tips: Enter all required values with appropriate units. Ensure all values are positive and within reasonable engineering ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of beam loading constant?
A: The beam loading constant depends on the specific loading configuration and distribution along the beam length.

Q2: How does support condition affect deflection?
A: Different support conditions (fixed, simply supported, cantilever) significantly influence beam deflection through the support condition constant.

Q3: What are acceptable deflection limits?
A: Deflection limits vary by application but typically range from L/180 to L/360 of the span length, where L is the beam span.

Q4: Why consider both bending and shear deformations?
A: For deep beams or certain materials, shear deformation can contribute significantly to total deflection and should not be neglected.

Q5: When is this formula most accurate?
A: This formula provides accurate results for straight, prismatic beams with linear elastic material behavior under static loading conditions.