Strength of Materials Notes for SSC JE Mechanical Engineering

Strength of materials studies how materials and machine parts behave when forces act on them. It is a core topic of the Mechanical Engineering paper in SSC JE, and it gives formula-based questions on stress, beams, torsion and columns. These strength of materials notes for SSC JE give the important formulas in tables, with solved examples and practice questions in simple language.

Stress and Strain

Example 1. A steel rod of area 100 mm² carries a pull of 20,000 N. Find the stress.
σ = 20,000 / 100 = 200 N/mm².

Elastic Constants

Stress-Strain Curve of Mild Steel

1. Proportional limit: stress and strain are proportional (Hooke's law).
2. Elastic limit: the material returns to its original shape after the load is removed.
3. Yield point: the material starts to deform permanently.
4. Ultimate stress: the maximum stress on the curve.
5. Breaking (fracture) point: the specimen breaks.

• Factor of safety = ultimate stress (or yield stress) / working stress.
• Ductile materials like mild steel show a large plastic deformation, while brittle materials like cast iron break suddenly.

Bending Moment and Deflection of Beams

• The bending moment is maximum where the shear force is zero.
• At the free end of a cantilever and at the supports of a simply supported beam, the bending moment is zero.

Bending and Torsion

Columns and Buckling

• Euler's buckling load: P = π² EI / (Le)².
• Slenderness ratio = effective length / least radius of gyration.

Thin Cylinders

• Hoop (circumferential) stress = pd / 2t.
• Longitudinal stress = pd / 4t.
• The hoop stress is twice the longitudinal stress, so a thin cylinder fails along the length first.

Quick Tips

• Learn the beam table of moments and deflections, because it is the most asked part.
• Always keep the units same: N, mm and N/mm².
• For columns, first find the effective length from the end condition.
• Remember that the hoop stress in a thin cylinder is double the longitudinal stress.

Quick Revision Points

• Stress = force / area and E = stress / strain.
• E = 2G (1 + μ) = 3K (1 − 2μ).
• Maximum BM in a simply supported beam with UDL is wL² / 8.
• Euler's load is P = π² EI / Le².
• Hoop stress = pd / 2t.

Practice Questions With Answers

1. What is the formula of normal stress?
   Answer: Force divided by area
2. What is the maximum bending moment of a simply supported beam with a central point load W and span L?
   Answer: WL / 4
3. What is the maximum bending moment of a cantilever with a point load W at the free end?
   Answer: WL
4. What is the effective length of a column with both ends fixed?
   Answer: L / 2
5. What is the effective length of a column with one end fixed and the other free?
   Answer: 2L
6. What is the relation between E, G and Poisson's ratio?
   Answer: E = 2G (1 + μ)
7. What is the moment of inertia of a rectangle about its centroidal axis?
   Answer: bd³ / 12
8. What is the hoop stress in a thin cylinder?
   Answer: pd / 2t
9. What is the unit of strain?
   Answer: No unit (a ratio)
10. What is the power transmitted by a shaft in terms of N and T?
    Answer: 2πNT / 60

How to Practise This Chapter

Solve two beam numericals and one torsion or column numerical daily and keep a formula sheet. Then solve questions from our practice papers and the previous year papers page. Read the previous chapter, Thermodynamics, and see all topics on the SSC JE Mechanical Engineering notes page. The Civil branch also uses these formulas in the Civil Engineering notes.

Frequently Asked Questions

What is strength of materials?

Strength of materials is the study of how materials resist the forces applied on them without failing.

What is stress and strain?

Stress is the internal resistance force per unit area, and strain is the change in length per unit original length.

What is Hooke's law?

Hooke's law says that within the elastic limit, stress is directly proportional to strain.

What is Young's modulus?

Young's modulus is the ratio of normal stress to linear strain and shows the stiffness of a material.

What is Poisson's ratio?

It is the ratio of lateral strain to longitudinal strain. For most metals it is about 0.25 to 0.33.

What is the relation between E, G and K?

E = 2G (1 + Poisson's ratio) and E = 3K (1 minus 2 times Poisson's ratio).

What is the bending equation?

The bending equation is M / I = sigma / y = E / R, where M is the bending moment, I is the moment of inertia and R is the radius of curvature.

What is the torsion equation?

The torsion equation is T / J = tau / r = G theta / L, which relates the twisting moment to the shear stress and the angle of twist.

What is Euler's buckling formula?

Euler's buckling load is P equals pi squared times E I divided by the square of the effective length.

What is the factor of safety?

It is the ratio of the ultimate or yield stress to the working stress of a member.

Is strength of materials important for SSC JE Mechanical?

Yes. It is a core subject and gives many formula-based questions every year.

How many questions come from strength of materials in SSC JE?

Usually four to seven questions come from strength of materials, but the number changes from year to year.