ENGINEERING – TRUCTURAL ENGINEERING β CONCRETE CALCULATOR
Deflection Long Term
A precise tool.
What is the Deflection Long Term & How does it work?
Longβterm deflection of reinforced concrete members is governed by the elastic response of the section combined with timeβdependent phenomena such as creep and shrinkage. The elastic component is calculated using the classic beam theory, where the modulus of elasticity of concrete (Ec) and the moment of inertia (I) of the crossβsection dominate the stiffness.
Creep, expressed by the creep coefficient ((phi)), enlarges the elastic strain under sustained loads, while shrinkage introduces an additional strain ((varepsilon_{sh})) that acts independently of external loading. Both effects are cumulative, leading to a deflection that can be significantly larger than the shortβterm elastic prediction.
The total longβterm deflection ((Delta_{lt})) is therefore obtained by augmenting the elastic deflection with the creep factor and adding the contribution from shrinkage strain over the member length. This approach provides a practical estimate for serviceability checks in concrete design.
\Delta_{lt} = \Delta_{elastic}(1+\phi) + \varepsilon_{sh} L
\Delta_{lt} = longβterm deflection (m)
\Delta_{elastic} = elastic deflection (m)
\phi = creep coefficient (unitless)
\varepsilon_{sh} = shrinkage strain (unitless)
L = span length (m)
\Delta_{elastic} = elastic deflection (m)
\phi = creep coefficient (unitless)
\varepsilon_{sh} = shrinkage strain (unitless)
L = span length (m)
Parameters
Result
β
Frequently Asked Questions
What factors affect long-term deflection in reinforced concrete?
Long-term deflection is influenced by the modulus of elasticity, moment of inertia, creep coefficient, and shrinkage.
How does creep affect concrete structures over time?
Creep causes concrete to deform under sustained loads, increasing its long-term deflection.
What is the role of shrinkage in calculating long-term deflection?
Shrinkage introduces additional strain by reducing the overall length of the concrete member over time.
How do I input the modulus of elasticity for concrete in this calculator?
Enter the modulus of elasticity (Ec) value specific to your concrete mix in the designated field.
Can this calculator account for temperature effects on deflection?
No, this calculator focuses on creep and shrinkage; it does not consider temperature effects.
What is the difference between elastic and long-term deflection in concrete?
Elastic deflection is immediate and reversible, while long-term deflection includes permanent deformations due to creep and shrinkage.
How often should I recalculate long-term deflection for a structure?
Recalculate periodically as conditions change or every 5-10 years for ongoing maintenance.
Results are for informational purposes only and do not constitute professional advice.