Strength of Materials & Theory of Structures

Product: Theory Subject
Categories: Diploma

Features Includes:

  • 137 - 3D/2D Animation
  • 644 Pages of Content
  • 90 Lecture Hours
  • 73 Solved Problems
  • 183 Quiz
  • Suitable for All Technical University Syllabus

Course Description

This learning solution provides the basics of strength of materials and structures. Basic concepts of simple bending, Beams and its deflection,Principle stresses, Planes, Mohr circle, Torsion, Springs, Cylinders, Columns,Dams, Retaining walls and frames stress are covered.In addition formulas are derived and problems are also solved with effective concepts

OBJECTIVES:

  • To understand principles, concepts and assumptions made in theory of simple bending
  • Comprehend the deflection of beam under loading
  • To know about Principal Stresses. Planes& Mohr‘s Circle
  • Comprehend the effect of pure torsion on solid and hollow circular shafts-springs
  • Understand the effect of effect of internal pressure on unrivetted thin cylinders
  • To understand the behaviour of columns under vertical loads.
  • To know the stability of retaining walls and dams under the action of lateral pressure
  • To understand effect on dead and live loads on statically determinate frames
UNIT I - THEORY OF SIMPLE BENDING

Introduction of Strength of materials (For Reference Only) - Introduction to beam - Bending moment and shear force - Sign convention - Types of beams based on supports - Geometric forms of beam - Relation between Loading, Shear Force and Bending Moment. Assumptions in theory of simple bending - Bending stress and neutral axis - Pure bending (or) simple bending - Moment of resistance. Theory of simple bending - Derivation of bending equation – Problems. Section modulus - Section modulus for symmetrical and unsymmetrical section - Section modulus for square section - Section modulus for rectangular section - Section modulus for circular section - Section modulus for triangular section - Section modulus for other section. Problem on section modulus - Calculation of section modulus for rectangular section - Calculation of section modulus for rectangular section - Calculation of section modulus for rectangular section - Calculation of section modulus for circular section - Calculation of section modulus for triangular section - Calculation of section modulus for triangular section - Calculation of section modulus for T- section. Problem on moment of resistance - Moment of resistance for rectangular section - Moment of resistance for square section - Moment of resistance for hollow rectangular section - Moment of resistance for circular section - Problems- Calculation of dimensions of section by simple bending theory - Problems. Calculation of bending stress - Calculation of bending stress for circular section - Calculation of bending stress for T-section - Calculation of bending stress for T-section - Calculations of bending stress for I-section - Calculation of bending stress for channel section. Calculation on loads on beam - Calculation on load on beam by simple bending theory - Calculation of load for built up section. Shear stress in beams - Shear stress distribution in beam. Shear stress distribution in rectangular section - Problems on shear stress - Calculation of load from shear stress. Shear stress distribution in circular section - Problems on circular section. Shear stress distribution in I section - Shear stress in I section - Problem on I section.

UNIT II - DEFLECTION OF BEAMS

Deflection of beam - Elastic curve of beam under normal load - Relationship between slope, deflection and curvature of beam. Double integration method - Methods of finding slope and deflection - Double integration method for cantilever beam - Cantilever beam with concentrated load at the end - Cantilever beam with uniformly distributed load. Double integration method for simply supported beam - Simply supported beam with concentrated load at mid span - Simply supported beam with uniformly distributed load throughout. Problems on double integration method - Problems on double integration method. Macaulay's method - Macaulay's method for simply supported beam - Simply supported beam with eccentric point load - Simply supported beam with uniformly distributed load. Macaulay's method for cantilever beam - Cantilever beam with point load at free end - Cantilever beam with uniformly distributed load over the entire span. Problem on Macaulay's method for simply supported beam - Simply supported beam with point load - Simply supported beam with uniformly distributed load. Problem on cantilever beam for finding slope and deflection - Cantilever beam with point loads - Cantilever beam with uniformly distributed load. Moment area method (Mohr’s theorem I and II) - Moment area method - Mohr's theorem for cantilever beam with point load - Cantilever beam with uniformly distributed load. Mohr's theorem for simply supported beam - Simply supported beam with point load - Simply supported beam with uniformly distributed load. Problems on Mohr's theorem - Cantilever beam with point load - Cantilever beam with uniformly distributed load- Problem on simply supported beam. Relationship between strength and stiffness - Stiffness of beam - Relationship between stress and deflection. Problem on relationship between strength and stiffness - Problem on relationship between strength and stiffness. Statically determinate and indeterminate structures - Statically determinate and indeterminate beam - Types of static indeterminacy. Propped cantilever beam - Problems on prop reactions. Problems on propped cantilever beam - Problems on prop reactions. Fixed and continuous beam - Fixed beam - Continuous beam.

UNIT III - PRINCIPAL STRESSES, PLANES AND MOHR'S CIRCLE

Principal stress - Introduction - Principal plane and stresses - A member subjected to a direct stress in one plane - The member is subjected to like direct stresses in two mutually perpendicular directions. Problem based on principal plane stresses - Problems. Importance of Mohr's circle - Mohr's circle - A body subjected to two mutually perpendicular principal tensile stresses of unequal intensities - A body subjected to two mutually perpendicular principal stresses which are unequal and unlike - A body is subjected to two mutually perpendicular principal tensile stresses accompanied by a simple shear stress. Problem based on Mohr's circle - Problems.

UNIT IV - TORSION AND SPRINGS

Torsion equation - Introduction to torsion - Polar moment of inertia and polar modulus - Assumptions in theory of pure torsion - Theory of pure torsion. Strength of shaft and shear stress distribution - Torsional rigidity - Strength of shaft - Shear stress distribution in shaft. Problems on torsion - Problem on hollow shaft - Comparison of hollow shaft and solid shaft - Problem on comparison of hollow shaft and solid shaft. Springs - Definition of spring - Commonly used spring materials - Classifications of springs. Closed coiled helical springs - Closed coiled or tension helical springs - Closed coiled helical springs with axial load - Problems.

UNIT V - THIN CYLINDERS

Thin Cylinders- Introduction - Thin cylindrical shells - Circumferential or hoop stresses - Longitudinal stresses - Maximum shear stress. Problem - Effect of internal pressure on the dimensions of a thin cylindrical shell - Problem.

UNIT VI - COLUMNS

Introduction to columns - Slenderness ratio - Classification of column - Failure of columns. Problems on slenderness ratio - Different end conditions of column - End conditions - Equivalent length of column. Euler's theory - Euler formula - Limitations for uses of Euler formula. Problems on Euler's theory - Column with both ends are hinged - Column with both ends are hinged - Column with both ends fixed - Column with one end fixed and other end free - Column with one end fixed and other end free - Column with one end fixed and other end hinged - Column with one end fixed and other end hinged. Design of column by using Euler's theory - Design of columns - Problems. Rankine's formula - Rankine's formula. Problems on Rankine's formula - Calculation of crippling load by rankine's formula - Problems - Calculation of safe load for I section. Comparison of crippling load - Comparison of Euler's theory and Rankine's theory - Calculation of ratio of Euler's and Rankine's critical loads. Design of column by Rankine's theory - Problem. Determination of Rankine's constant

UNIT VII - DAMS AND RETAINING WALLS

Dams - Gravity dams - Forces acting on the gravity dams. Stresses at the base of the dam - Analysis of dam - Stress distribution at the base of gravity dams - Problems based on middle third rule. Calculation of stresses at the base of the dam - Analysis of stress at the base of dam - Problems. Minimum base width and stability condition of the dam - Minimum bottom width for economical dam section - Stability of dam. Problem based on stability condition of the dam - Problems based on minimum base width - Steps for determining the minimum base width - Calculation of minimum base width. Retaining walls - Retaining walls - Active and passive earth pressure - Rankine's theory of earth pressure - Retaining wall with surcharge. Problem on base pressure acting on retaining wall - Forces acting on retaining wall - Calculation of base pressure acting on retaining wall - Calculation of base pressure for retaining wall with surcharge. Problem on stability of retaining wall - Base width calculation for retaining wall - Base width calculation.

UNIT VIII - STRESSES IN FRAMES

Different types of frame structures - Introduction to frame structures - Types of Framed Structures. Problems based on classification of frames - Steps for classification of frames - Problems. Analysis of frames - Methods of analysis of frames - Method of joints - Analysis of simple frame by method of joints. Analysis of frames by method of joints - Steps for analysis of frames by method of joints - Analysis of simply supported frame by method of joints - Problems. Analysis of cantilever frames by method of joints - Steps for analysis of cantilever frames by method of joints - Problems. Method of sections - Analysis of simple frame by method of sections. Analysis of simply supported frames by method of sections – Problems-Steps for analysis of cantilever frames by method of section - Analysis of cantilever frame by method of sections - Problems.