Creep Coefficient Calculator

The Creep Coefficient Calculator is a tool used in structural engineering to determine the creep coefficient of concrete, which measures the long-term deformation of concrete under sustained load. This metric is crucial for designing durable and safe concrete structures, as it helps predict how concrete will behave over time under various conditions such as humidity and loading age.

By calculating the creep coefficient, engineers can evaluate potential structural deformations and take necessary steps to mitigate risks in construction projects.

Formula of Creep Coefficient Calculator

The creep coefficient, denoted as φ(t, t₀), is calculated using the following formula:

Where:

• φ(t, t₀) is the creep coefficient at time t for loading applied at time t₀.
• φ₀ is the notional creep coefficient, which depends on factors like relative humidity, concrete strength, and age at loading.
• β_c(t, t₀) describes the development of creep over time after loading.

Notional Creep Coefficient (φ₀)

The notional creep coefficient φ₀ is determined by:

φ₀ = φ_RH × β(f_cm) × β(t₀)

Where:

1. φ_RH accounts for the effect of relative humidity: φ_RH = 1 + [(1 – RH/100) / (0.1 × √h₀³)]
   • RH is the relative humidity of the environment (in percent).
   • h₀ is the notional size of the member, calculated as: h₀ = 2 × (A_c / u)
     • A_c is the cross-sectional area of the concrete member (in mm²).
     • u is the perimeter of the member in contact with the atmosphere (in mm).
2. β(f_cm) accounts for the effect of concrete strength: β(f_cm) = 16.8 / √f_cm
   • f_cm is the mean compressive strength of concrete at 28 days (in MPa), calculated as: f_cm = f_ck + 8
     • f_ck is the characteristic compressive strength of concrete (in MPa).
3. β(t₀) accounts for the age of concrete at loading: β(t₀) = 1 / [0.1 + (t₀)⁰²]
   • t₀ is the age of concrete at the time of loading (in days).

Development Coefficient (β_c(t, t₀))

The coefficient β_c(t, t₀) describes how creep develops over time:

β_c(t, t₀) = [(t – t₀) / (β_H + t – t₀)]⁰³

Where:

• t is the age of concrete at the moment considered (in days).
• t₀ is the age of concrete at loading (in days).
• β_H is a coefficient depending on relative humidity (RH) and notional member size (h₀): β_H = 1.5 × [1 + (0.012 × RH)¹⁸] × h₀ + 250

General Terms Table

Below is a table summarizing key variables used in creep coefficient calculations:

Variable	Definition
RH	Relative Humidity (percent)
h₀	Notional size of the concrete member (mm)
A_c	Cross-sectional area of the concrete member (mm²)
u	Perimeter in contact with the atmosphere (mm)
f_ck	Characteristic compressive strength of concrete (MPa)
f_cm	Mean compressive strength of concrete at 28 days (MPa)
t, t₀	Age of concrete at time of observation and loading (days)

Example of Creep Coefficient Calculator

Let’s calculate the creep coefficient for the following conditions:

• Relative Humidity (RH): 60%
• Cross-sectional Area (A_c): 300000 mm²
• Perimeter (u): 2400 mm
• Characteristic Strength (f_ck): 30 MPa
• Age at Loading (t₀): 28 days
• Observation Time (t): 365 days

Steps:

1. Calculate h₀: h₀ = 2 × (A_c / u) = 2 × (300000 / 2400) = 250 mm
2. Calculate φ_RH: φ_RH = 1 + [(1 – 60/100) / (0.1 × √250³)] = 1 + [(0.4) / (39.53)] = 1.01
3. Calculate β(f_cm): f_cm = f_ck + 8 = 30 + 8 = 38 MPa β(f_cm) = 16.8 / √38 = 2.73
4. Calculate β(t₀): β(t₀) = 1 / [0.1 + (28)⁰²] = 1 / 1.532 = 0.65
5. Calculate φ₀: φ₀ = φ_RH × β(f_cm) × β(t₀) = 1.01 × 2.73 × 0.65 = 1.79
6. Calculate β_c(t, t₀): β_H = 1.5 × [1 + (0.012 × 60)¹⁸] × 250 + 250 = 625.4 β_c(t, t₀) = [(365 – 28) / (625.4 + 365 – 28)]⁰³ = 0.27
7. Calculate φ(t, t₀): φ(t, t₀) = φ₀ × β_c(t, t₀) = 1.79 × 0.27 = 0.48

The creep coefficient is approximately 0.48.

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