---
title: "Percent strength gain at 14 days"
subject: "Concrete Technology and Masonry Structure"
chapter: 4
key: "semester_5/concrete_technology_and_masonry_structure:strength-gain-14-days"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/strength-gain-14-days
site: BCT Engineering
---

# Percent strength gain at 14 days

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

- Asked in: 2066 Chaitra (old course), 5 marks
- Video: [Percentage strength of concrete at various ages by bangla](https://www.youtube.com/watch?v=gbw0EaJtskI) — Zahidul Islam
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/strength-gain-14-days
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4

## Question

Calculate the percent of strength gain of a moist cured concrete containing 500 gm cement and 0.45 w/c ratio at the age of 14 days, if 90% of the 28 days hydration takes place at 14 days normal curing.

## Short answer

Using Powers' model with α=1 at 28 days and α=0.9 at 14 days, w/c=0.45. Strength at 28 days is 149.7 MPa, at 14 days 123.9 MPa, so the percent gain is 82.8% of the 28-day strength.

## 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.

#### Reading of the question
The hydration at 28 days is taken as complete ($\alpha_{28} = 1.0$) and at 14 days $\alpha_{14} = 0.9$ (90% of that at 28 days). Cement = 500 g, $w/c = 0.45$ (the mass cancels in the ratio). "Percent strength gain" is the strength at 14 days as a percentage of the 28-day strength.

#### 28 days ($\alpha = 1$)
$$
x_{28} = \frac{0.657}{0.319+0.45} = 0.854, \qquad f_{28} = 240\times0.854^3 = 149.7\ \text{MPa}
$$

#### 14 days ($\alpha = 0.9$)
$$
x_{14} = \frac{0.657\times0.9}{0.319\times0.9+0.45} = \frac{0.5913}{0.7371} = 0.802, \qquad f_{14} = 240\times0.802^3 = 123.9\ \text{MPa}
$$

$$
\frac{f_{14}}{f_{28}} = \frac{123.9}{149.7}\times100 = 82.8\%
$$

**Answer: the concrete gains about 82.8% of its 28-day strength at 14 days** (123.9 MPa against 149.7 MPa). Note that 90% hydration gives only about 83% strength because of the cubic relation.

## Check yourself

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

1. How is percent strength gain defined here?
   A. Strength at 14 days as a percentage of strength at 28 days
   B. 28-day strength minus 14-day strength
   C. Strength at 28 days divided by 14 days strength
   D. Hydration at 14 days as a percentage
   Answer: A. The 14-day strength is compared with the 28-day strength. (Key point: Reading of question)

2. What alpha values are used for 28 and 14 days?
   A. 0.9 at 28 days and 0.81 at 14 days
   B. 1.0 at 14 days and 0.9 at 28 days
   C. 1.0 at 28 days and 0.9 at 14 days
   D. 0.5 at 14 days and 1.0 at 28 days
   Answer: C. 28-day hydration is taken as complete; 14 days has 90% of that. (Key point: Degrees of hydration)

3. Does the 500 g cement mass affect the result?
   A. Yes, strength is proportional to mass
   B. Yes, it changes alpha
   C. Yes, it changes the 240 MPa constant
   D. No, it cancels; only w/c = 0.45 matters
   Answer: D. Gel and space scale with mass, so x depends on alpha and w/c only. (Key point: Cement mass)

4. The 14-day strength is about what percent of the 28-day strength, and why not 90%?
   A. 90%; strength is proportional to hydration
   B. 82.8%; the cubic relation magnifies the drop in x
   C. 95%; hydration is almost complete
   D. 60%; strength is proportional to x^3 of alpha
   Answer: B. 123.9/149.7 = 82.8%; x falls from 0.854 to 0.802, and cubing amplifies it. (Key point: Result)

## Related in Concrete Technology and Masonry Structure

- [Theoretical strength of moist cured concrete (1 kg cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Atheoretical-strength-1kg-cement) — Concrete Technology and Masonry Structure, chapter 4
- [Gel/space ratio and strength (550 gm cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Agel-space-ratio-550g) — Concrete Technology and Masonry Structure, chapter 4, asked 3×
- [Gel/space ratio and strength (600 gm cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Agel-space-ratio-600g) — Concrete Technology and Masonry Structure, chapter 4, asked 3×
- [Capillary porosity of hydrated cement (28 days)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acapillary-porosity-28-days) — Concrete Technology and Masonry Structure, chapter 4, asked 2×
- [Strength of paste: 300 gm cement](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acement-strength-300g-150g) — Concrete Technology and Masonry Structure, chapter 4

## Related in other subjects

- [Why hydration of cement takes place](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Ahydration-of-cement-why) — Civil Engineering Materials, chapter 5