SOLID MECHANICS (1BCV303)

SOLID MECHANICS

Course Code 1BCV303 
Scheme 2025
Type of Course Professional Core Course (PCC) 
Semester III
Teaching Hours/Week (L:T:P) 70 (42:28:0:50) 
CIE Marks 50
Total Hours of Pedagogy per Semester CI(L /T): LI(P):TW&SL 120(42:28:0:50)
SEE Marks 50
Credits 4 
Total Marks 100
Examination type (SEE) Theory 
Exam Hours 03

Module-1

Introduction, stress–strain and axial members:

• Concepts of rigid and deformable bodies; elastic and plastic behaviour; normal and shear stresses; normal and shear strains.

• Stress–strain curves for ductile and brittle materials (qualitative); proportional limit, yield point, ultimate and failure.

• Hooke’s law for uniaxial stress; elastic constants: E, G, K, ν and their relationships (isotropic, homogeneous material).

• Axially loaded members: bars of uniform and varying cross-section; stepped bars; temperature stresses (simple cases with/without constraints).

• Factor of safety and working stress concept (introductory).

Linked COs: CO1, CO2 Number of Hours: 14

Module-2

Shear force, bending moment and stresses in beams:

• Types of loads and supports; concept of shear force (SF) and bending moment (BM).

• SF and BM diagrams for statically determinate beams: simply supported, cantilever and overhanging beams with point loads, UDL/UVL and simple combinations. Relationship between load, SF and BM diagrams.

• Flexural ( bending) s t r e s s e s : assumptions of s i m p l e b e n d i n g t h e o r y ; f l e x u r e

Linked COs: CO2, CO3 Number of Hours:14

Module-3

Torsion and combined stresses:

• Torsion of circular shafts: assumptions; torsion formula 

(statement and application); solid and hollow shafts, strength and stiffness comparisons.

• Power transmitted by shafts; design-style numericals (within course level).

• Combined axial and bending stresses in members (qualitative introduction + simple numericals).

• Introduction to thin cylindrical shells under internal pressure: hoop and longitudinal stresses (formulae and simple problems).

Linked COs: CO2, CO3, CO6 Number of Hours:14

Module-4

Two-dimensional stress analysis and Mohr’s circle:

• Plane stress at a point: normal and shear stresses on inclined planes; transformation equations (no full derivation needed at length).

• Principal planes and principal stresses; maximum shear stress; orientation of principal planes.

• Construction and use of Mohr’s circle for plane stress – determination of principal stresses and maximum shear; interpretation in terms of material failure.

• Plane strain (basic idea); brief mention of 3D generalisation (qualitative).

Linked COs: CO1, CO4, CO6 Number of Hours: 14

Module-5

Columns, buckling and strain energy:

• Columns and struts: classifications; slenderness ratio; Euler’s buckling theory for ideal columns (pinned–pinned, fixed–free, fixed–pinned, fixed–fixed).

• Critical load, effective length and factor of safety in compression members; limitations of Euler theory.

• Introduction to empirical/Rankine or IS-based formula (statement and awareness).

• Strain energy: concept of energy stored in axially loaded members and in members under bending and torsion (formulae and simple numericals).

• Qualitative use of strain-energy methods for deflection and impact (no lengthy derivations); link to stiffness and serviceability checks.

Linked COs: CO5, CO6 Number of Hours:14

Suggested Learning Resources

Text books:

1. Beer, F. P., Johnston, E. R., DeWolf, J. T., & Mazurek, D. F. Mechanics of Materials. McGraw-Hill Education. Latest edition.

2. Hibbeler, R. C. Mechanics of Materials. Pearson. Latest edition.

3. Punmia, B. C., Jain, A. K., & Jain, A. K. Strength of Materials. Laxmi Publications.

Reference books / Manuals:

1. Ramamrutham, S. Strength of Materials. Dhanpat Rai Publishing.

2. Gere, J. M., & Goodno, B. J. Mechanics of Materials. Cengage.

3. Timoshenko, S., & Young, D. H. Elements of Strength of Materials.