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**STRENGTH OF MATERIALS – I **

Course Objectives

1. Understand the concept of simple stress and strain.

2. Understand different types of direct stresses and strains.

3. Understand stress- strain diagram. Hookes law, Poisson’s ratio. Young’s Modulus of Elasticity.

4. Compute simple stresses and strains in bars of uniform and varying sections subjected to axial loads.

5. Derive relationship between the Elastic Moduli.

6. Compute stresses and strains in compound bars subjected to axial loads and temperature variations.

7. Compute combined stresses and strains at a point across any plane in a two dimensional system.

8. Understand the concept of principal planes and principal stresses.

9. Apply graphical and analytical methods to compute principal stresses and strain and locate principal planes.

10. Derive mathematically the Torsion Equation.

11. Apply the Torsion equation to compute torsional stresses in solid and hollow shafts.

12. Compute principal stresses and maximum shear stresses in circular shafts subjected to combined stresses.

13. Analyze stresses in close- coiled helical springs.

14. Analyze stresses in thin shells and spheres subjected to internal pressure.

15. Apply different formulae to analyze stresses in struts and columns subjected to axial loads.

16. Compute bending moments and shear forces at different sections of determinate beam structures subjected to different types of loading and sketch their distribution graphically.

17. Derive mathematically the relationship between the rate of loading, shear force and bending moment at any section of a beam.

18. Understand the theory of simple bending.

19. Apply the theory of simple bending to compute stresses in beams of homogenous and composite sections of different shapes.

20. Derive relationship between moment slope and deflection.

21. Use the above relationship and other methods to calculate slope and deflection in beams.

22. Compute stresses in determine trussed frames and roof trusses.

Detailed Contents

1. Simple stresses and strains : Concept of stress and strain; St. Vernants principle, stress and strain diagram, Hooke’s law, Young’s modulus, Poisson ratio, stress at a point, stress and strains in bars subjected to axial loading. Modulus of elasticity, stress produced in compound bars subject to axial loading.Temperature stress and strain calculations due to applications of axial loads and variation of temperature in single and compound bars. Compound stress and strains, the two dimensional system; stress at a point on a plane, principal stresses and principal planes; Mohr’s circle of stress; ellipse of stress and their applications. Generalized Hook's Law, principal stresses related to principal strains

2. Bending moment and shear force diagrams: S.F and B.M definitions. BM and PTU/BOS/ME/101/10-06-2005/BATCH-2004 8 SF diagrams for cantilevers, simply supported beams with or without overhangs and calculation of maximum BM and SF and the point of contraflexure under the following loads:

a) Concentrated loads

b) Uniformity distributed loads over the whole span or part of span

c) Combination of concentrated loads (two or three) and uniformly distributed loads

d) Uniformity varying loads

e) Application of moments Relation between rate of loading, shear force and bending moment

3. Theory of bending stresses in beams due to bending: assumptions in the simple bending theory, derivation of formula: its application to beams of rectangular, circular and channel, I & T- sections,: Combined direct and bending stresses in aforementioned sections, composite / flitched beams.

4. Torsion : Derivation of torsion equation and its assumptions. Applications of the equation to the hollow and solid circular shafts, torsional rigidity, combined torsion and bending of circular shafts principal stress and maximum shear stresses under combined loading of bending and torsion, analysis of close-coiled-helical springs.

5. Thin cylinders and spheres : Derivation of formulae and calculation of hoop stress, longitudinal stress in a cylinder, effects of joints, change in diameter, length and internal volume; principal stresses in sphere and change in diameter and internal volume

6. Columns and struts : Columns and failure of columns : Euler’s formuls; RankineGordon’s formula, Johnson’s empirical formula for axially loaded columns and their applications.

7. Slope and deflection : Relationship between moment, slope and deflection, Moment area method; method of integration; Macaulay’s method: Use of all these methods to calculate slope and deflection for the following :

a) Cantilevers

b) Simply supported beams with or without overhang

c) Under concentrated loads, uniformly distributed loads or combination of concentrated and uniformly distributed loads

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