Stress, Strain, Elastic Constants & Rectifiers

Concept Notes

Part A – Strength of Materials

1. Stress

Definition: Resistance offered by a body per unit area when an external force is applied.
Formula:
$\sigma = \frac{P}{A}$
where
PPP = load, AAA = area.
Types: Tensile, Compressive, Shear.

Example: A rod of area 200 mm2200 \, mm^2200mm2 carries 40 kN load.

$\sigma = \frac{40 \times 10^3}{200 \times 10^{-6}} = 200 , MPa$

2. Strain

Definition: Ratio of change in dimension to original dimension.

$\varepsilon = \frac{\Delta L}{L}$

Example: A bar of 2 m elongates by 1 mm.

$\varepsilon = \frac{1}{2000} = 0.0005$

3. Hooke’s Law

Within elastic limit,

$\sigma \propto \varepsilon \quad \Rightarrow \quad \sigma = E \varepsilon$

4. Elastic Constants

Young’s Modulus:

$E = \frac{\sigma}{\varepsilon}$

Shear Modulus (Rigidity):

$G = \frac{\tau}{\gamma}$

Bulk Modulus:

$K = \frac{p}{\Delta V/V}$

Poisson’s Ratio:

$\mu = -\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}$

Relations:
$E = 2G(1+\mu)$
$E = 3K(1-2\mu)$
$\frac{E}{G} = 2(1+\mu)$

$\frac{E}{K} = 3(1-2\mu)$

Part B – Rectifiers

Though an Electronics concept, basics are often asked for inter-disciplinary awareness.

1. Introduction

A rectifier converts AC → DC.
Used in power supplies for civil lab instruments, survey equipment, etc.

2. Half-Wave Rectifier (HWR)

Uses one diode.
Output: Pulsating DC.
Average DC value:

$V_{dc} = \frac{V_m}{\pi}$

RMS value:

$V_{rms} = \frac{V_m}{2}$

Rectification efficiency:

$\eta = \frac{0.406}{1} = 40.6%$

3. Full-Wave Rectifier (FWR)

Uses two diodes (center-tap) or four diodes (bridge).
Output: Continuous DC pulses.
Average DC value:

$V_{dc} = \frac{2V_m}{\pi}$

RMS value:

$V_{rms} = \frac{V_m}{\sqrt{2}}$

Efficiency:

$\eta = 81.2%$

4. Ripple Factor

Represents AC present in DC output.

$r = \frac{V_{rms(ac)}}{V_{dc}}$

HWR: $r = 1.21$

FWR: $r = 0.482$

5. Peak Inverse Voltage (PIV)

Maximum reverse voltage a diode can withstand.
HWR: $PIV = V_m$
FWR (center-tap): $PIV = 2V_m$
Bridge Rectifier: $PIV = V_m$

⚙️ Formulas

$\sigma = \frac{P}{A}$
$\varepsilon = \frac{\Delta L}{L}$
$\sigma = E \varepsilon$
$E = \frac{\sigma}{\varepsilon}$
$G = \frac{\tau}{\gamma}$
$K = \frac{p}{\Delta V/V}$
$\mu = -\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}$
$E = 2G(1+\mu)$
$E = 3K(1-2\mu)$
$V_{dc(HWR)} = \frac{V_m}{\pi}$
$V_{dc(FWR)} = \frac{2V_m}{\pi}$
$V_{rms(HWR)} = \frac{V_m}{2}$
$V_{rms(FWR)} = \frac{V_m}{\sqrt{2}}$
$\eta_{HWR} = 40.6%$
$\eta_{FWR} = 81.2%$
$r_{HWR} = 1.21$
$r_{FWR} = 0.482$
$PIV_{HWR} = V_m$
$PIV_{FWR} = 2V_m$

$PIV_{Bridge} = V_m$

🔟 10 MCQs

Q1. Stress is load per _____.
a) Length
b) Area
c) Volume
d) Modulus

Q2. A rod elongates by 0.5 mm for length 1 m. Find strain.
a) 0.0005
b) 0.005
c) 0.05
d) 0.5

Q3. Hooke’s law holds good up to:
a) Yield point
b) Elastic limit
c) Ultimate stress
d) Plastic range

Q4. A 100 mm² rod carries 20 kN. Stress = ?
a) 200 MPa
b) 100 MPa
c) 20 MPa
d) 2 MPa

Q5. Poisson’s ratio is:
a) Stress/Strain
b) Lateral strain/Longitudinal strain
c) Load/Area
d) Shear stress/Shear strain

Q6. Average DC output of Half-Wave Rectifier is:
a) $\frac{V_m}{2}$
b) $\frac{V_m}{\pi}$
c) $\frac{2V_m}{\pi}$
d) $\frac{V_m}{\sqrt{2}}$

Q7. Efficiency of Full-Wave Rectifier is:
a) 40.6%
b) 50%
c) 81.2%
d) 90%

Q8. Ripple factor of Half-Wave Rectifier is:
a) 1.21
b) 0.482
c) 1.0
d) 0.812

Q9. PIV for Bridge Rectifier = ?
a) $V_m$
b) $2V_m$
c) $V_m/2$
d) $\sqrt{2} V_m$

Q10. Relation between E and G is:
a) $E = G(1+\mu)$
b) $E = 2G(1+\mu)$
c) $E = 3G(1-2\mu)$
d) $E = \frac{G}{1+\mu}$

✅ Answer Key

Q	Answer
1	b
2	a
3	b
4	a
5	b
6	b
7	c
8	a
9	a
10	b

🧠 Explanations

Q1: Stress = Load/Area → (b).
Q2: Strain = 0.5/1000 = 0.0005 → (a).
Q3: Hooke’s law valid up to elastic limit → (b).
Q4: Stress = 20×10³ / 100×10⁻⁶ = 200 MPa → (a).
Q5: Poisson’s ratio = lateral strain / longitudinal strain → (b).
Q6: HWR DC output = Vm/π → (b).
Q7: FWR efficiency = 81.2% → (c).
Q8: Ripple factor HWR = 1.21 → (a).
Q9: Bridge rectifier PIV = Vm → (a).
Q10: Correct relation: E = 2G(1+μ) → (b).

🎯 Motivation / Why Practice Matters

For ECET 2026, both Civil Core (SOM) and Basic Electronics (Rectifiers) may appear in mixed sections.

Stress–strain is a high-weightage topic forming base for RCC, Theory of Structures.
Rectifiers are small but scoring – formula-based questions often come.
👉 If you master formulas + concepts, these become your “easy marks.”

📲 CTA

🔥 Join our WhatsApp Group for free Civil ECET 2026 notes, quizzes & materials:
👉 Join Here

Post Views: 11

LATEST NEWS

Day 10 Work Study – ECET 2026 Mechanical

Day 10 Environmental Engineering – Sedimentation & Filtration (ECET 2026 Civil)

CONTACTS

Day 1 Strength of Materials – Stress, Strain, Elastic Constants + Rectifiers (ECET 2026 Civil)

Concept Notes

Part A – Strength of Materials

1. Stress

2. Strain

3. Hooke’s Law

4. Elastic Constants

Part B – Rectifiers

1. Introduction

2. Half-Wave Rectifier (HWR)

3. Full-Wave Rectifier (FWR)

4. Ripple Factor

5. Peak Inverse Voltage (PIV)

⚙️ Formulas

🔟 10 MCQs

✅ Answer Key

🧠 Explanations

🎯 Motivation / Why Practice Matters

📲 CTA

Day 10 Environmental Engineering – Sedimentation & Filtration (ECET 2026 Civil)

Day 10 Transportation Engineering – Highway Materials (ECET 2026 Civil)

Leave a comment Cancel reply

Contacts

Important Links

Follow Us

LATEST NEWS

CONTACTS

Day 1 Strength of Materials – Stress, Strain, Elastic Constants + Rectifiers (ECET 2026 Civil)

Concept Notes

Part A – Strength of Materials

1. Stress

2. Strain

3. Hooke’s Law

4. Elastic Constants

Part B – Rectifiers

1. Introduction

2. Half-Wave Rectifier (HWR)

3. Full-Wave Rectifier (FWR)

4. Ripple Factor

5. Peak Inverse Voltage (PIV)

⚙️ Formulas

🔟 10 MCQs

✅ Answer Key

🧠 Explanations

🎯 Motivation / Why Practice Matters

📲 CTA

Related Posts

Leave a comment Cancel reply

Contacts

Important Links

Follow Us