---
title: "Theoretical strength of moist cured concrete (1 kg cement)"
subject: "Concrete Technology and Masonry Structure"
chapter: 4
key: "semester_5/concrete_technology_and_masonry_structure:theoretical-strength-1kg-cement"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/theoretical-strength-1kg-cement
site: BCT Engineering
---

# Theoretical strength of moist cured concrete (1 kg cement)

Concrete Technology and Masonry Structure · Chapter 4: Properties of hardened concrete

- Asked in: 2067 Ashadh (old course), 5 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/theoretical-strength-1kg-cement
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4

## Question

Calculate the theoretical strength of moist cured concrete containing 1 kg of cement with 0.5 w/c ratio at the age of 28 days. Assume 90% hydration is completed in 28 days.

## Short answer

Powers' model: gel/space ratio x = 0.657α/(0.319α + w/c). With w/c=0.5 and 90% hydration (α=0.9), x = 0.751, giving theoretical compressive strength 101.7 MPa.

## Answer

Powers' model gives the strength of concrete in terms of the **gel/space ratio** $x$:

$$
x = \frac{\text{volume of gel}}{\text{volume of gel} + \text{capillary pores}} = \frac{0.657\,\alpha}{0.319\,\alpha + w/c}
$$

where $\alpha$ is the degree of hydration and $w/c$ the water-cement ratio by mass. The numbers come from cement of specific gravity about 3.14: 1 g of cement has 0.319 cm$^3$ volume and produces gel of $2.06\times0.319 = 0.657$ cm$^3$ (including gel pores). Compressive strength:

$$
f_c = 240\,x^3\ \text{MPa}
$$

(240 MPa is the intrinsic strength of the gel; it varies from about 234 to 255 MPa for different cements.) The ratio $x$ does not depend on the mass of cement; the mass is only needed to give volumes.

#### Given
Cement = 1 kg; $w/c = 0.5$ (water = 0.5 kg); hydration at 28 days $\alpha = 0.9$.

$$
\begin{aligned} x &= \frac{0.657\times0.9}{0.319\times0.9+0.5} = \frac{0.5913}{0.7871} = 0.751 \\ f_c &= 240\times0.751^3 = 101.7\ \text{MPa} \end{aligned}
$$

(Volumes for 1 kg: gel $= 1000\times0.657\times0.9 = 591.3$ cm$^3$; space $= 1000\times0.319\times0.9 + 500 = 787.1$ cm$^3$; ratio 0.751.)

**Answer: gel/space ratio = 0.751 and theoretical strength at 28 days = 101.7 MPa.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which alpha and w/c are used for 1 kg cement at 28 days?
   A. alpha = 0.9, w/c = 0.5
   B. alpha = 1.0, w/c = 0.5
   C. alpha = 0.9, w/c = 0.9
   D. alpha = 0.5, w/c = 0.9
   Answer: A. Hydration is 90% at 28 days and water is 0.5 kg for 1 kg cement. (Key point: Inputs)

2. The gel/space ratio is:
   A. 0.657/0.819 = 0.802
   B. 0.5913/0.7871 = 0.751
   C. 0.5913/0.5 = 1.18
   D. 0.7871/0.5913 = 1.33
   Answer: B. x = 0.657(0.9)/(0.319(0.9)+0.5) = 0.751. (Key point: Gel/space ratio)

3. Theoretical strength at 28 days is about:
   A. 123.9 MPa
   B. 180 MPa
   C. 101.7 MPa
   D. 50 MPa
   Answer: C. 240 x 0.751^3 = 101.7 MPa. (Key point: Strength)

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