DI03006041 · Semester 3 · 5G scheme
Mechanics of Structures-I
Notes and solutions following the Gujarat Technological University (GTU) syllabus for DI03006041. Independent material — not issued by the university.
Materials
Complete Book
The whole syllabus, unit by unit, written for the exam.
Complete Book
118 pages
Premium Preview · 12 pages
Past Papers
Original question papers from previous exams.
PYQ Solutions
Past university papers, fully solved.
Solved past papers — detailed answers
39 pages · English + ગુજરાતી
Premium Preview · 3 pages
Syllabus units
Unit 1: Direct Stress & Strain
- Direct stress, Linear strain, Elasticity, Elastic limit, Hook's law, Modulus of Elasticity or Young's modulus, Stress Strain curve for mild steel bar under tension with numerical problems.
- Lateral stress and strain, Poisson's ratio, Volumetric strain, Bulk modulus, relation between three moduli and numericals.
- Basics Concepts of Shear Stress , Shear Strain & Modulus of rigidity.
- Concept of composite and compound section, modular ratio and numericals.
- Concept of Thermal stress and strain, Thermal stresses for non-yielding and yielding condition with numericals.
- Stresses due to gradual, sudden and impact load, corresponding deformation, Strain energy, Resilience, Proof resilience and Modulus of resilience with numericals.
Unit 2: Moment of Inertia
- Importance of Moment of Inertia.
- Axis of symmetry, Centroidal axis and axis of reference.
- Parallel Axis Theorem & Perpendicular Axis Theorem
- Formulas to calculate Moment of Inertia of solid and hollow rectangle, square, circle, triangle shapes (without derivations).
- Moment of Inertia of symmetrical and asymmetrical I-section, Channel section, T-section, Angle section, Hollow sections and Built up sections about Centroidal axis and any other reference axis using Parallel axis theorem.
- Polar Moment of Inertia of solid & hollow circular sections.
Unit 3: S.F. & B. M. in Beam
- Statically Determinate and statically indeterminate beam examples.
- Concept of Bending Moment and Shear Force in beam.
- Sagging and Hogging Bending Moment. Positive and Negative Shear Force.
- Calculation of Bending Moment and Shear Force at various sections of cantilever, simply supported and overhang beam subjected to point load and/ or u.d.l.
- S.F. & B.M. Diagram for above beams
- Point of Contra-flexure & its importance.
Unit 4: Bending & Shear Stress in Beam
- Concept and theory of pure bending, assumptions, Bending equation (without derivation), Section Modulus, Bending stresses and their nature, Bending stress distribution diagram.
- Concept of moment of resistance and simple numerical problems using bending equation.
- Shear stress equation (without derivation), relation between maximum and average Shear stress for rectangular and circular section.
- Shear stress distribution for square, rectangular, circle, hollow square, rectangular, circular, angle sections, channel section, I- section, T section. Simple numerical problems based on Shear equation.
Unit 5: Slope and Deflection
- Concept of Slope & Deflection of beams.
- Flexural rigidity and its significance.
- Formulas (without derivation) of maximum slope & deflection for cantilever beams subjected to point load at free end and u.d.l. Over the entire span.
- Formulas (without derivation) of maximum slope & deflection for simply supported beams subjected to point load at center and u.d.l. over the entire span.
Unit 6: Analysis of Truss
- Type of truss - Simple, fink, compound fink, Howe truss, Pratt truss, North light truss, king post truss, queen post truss, French truss. Compare the simple truss with the beam.
- Perfect, deficient and redundant truss.
- Analysis of different trusses to find out axial forces in members using analytical method (method of joint) and graphical method.
Unit 7: Column & Strut
- Column and Strut, radius of gyration, slenderness ratio, Short Column and Long Column.
- End conditions & effective length of column. Mode of failure in column.
- The limitations of Euler's theory for short column, Euler's formula for crippling load of long columns and numericals.
- Rankin's formula for buckling load of short & long columns and numericals.
About this course
After learning Mechanics of rigid bodies in the 2 nd semester as a course Engineering Mechanics, Mechanics of Structures-I is introduced in 3 rd semester which mainly deals with analysis of deformable structures. The primary purpose of the study of this course is to understand the behaviour of various structural elements like beams, columns and truss members (struts/ties) under direct and transverse loads. Study of slope and deflection of beams will give insight to students about 'Stiffness', a very important property of the structure. This course enables the student to analyse the determinate structure and this will be helpful for safe and economical design of Steel & Concrete Structures used in Civil Engineering construction.