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Note for Strength Of Materials - SOM By simran arya

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Strength of Materials Contents Sl. No. Chapter - 1 Topic Stress and Strain • • • • • • Chapter - 2 Principal Stress and Strain • • • • • • Chapter - 3 Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Moment of Inertia and Centroid • • • • • • Chapter - 4 Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Bending Moment and Shear Force Diagram • • • • • • Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Page No. 1 1 23 27 37 45 53 64 64 102 105 112 118 126 135 135 146 147 148 149 150 151 151 194 198 209 218 228

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Strength of Materials India’s No 1 IES Academy Sl. No. Chapter - 5 Topic Deflection of Beam • • • • • • Chapter - 6 Chapter - 7 • • • • • • Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Fixed and Continuous Beam Theory at a Glance (for IES, GATE, PSU) Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Thin Cylinder • • • • • • Page No. 240 240 277 277 281 283 286 289 289 294 295 300 304 307 313 313 317 317 320 323 326 327 327 332 333 334 336 337 Torsion • • • • • • Chapter-10 Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Shear Stress in Beam • • • • • Chapter - 9 Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Bending Stress in Beam • • • • • • Chapter - 8 Contents Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers 337 346 347 356 360 367 376 376 379 380 383 386 390 Page-ii ________________________________________________________________________ www.iesacademy.com Email: iesacademy@yahoo.com 25, 1st Floor, Jia Sarai, Near IIT. New Delhi-16 Ph: 011-26537570, 9810958290

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Strength of Materials India’s No 1 IES Academy Sl. No. Chapter-11 Topic Thick Cylinder • • • • • • Chapter-12 Chapter-13 • • • • • • Chapter-16 Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Strain Energy Method Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Theories of Failure • • • • • • Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Riveted and Welded Joint • • • • • • Page No. 393 393 402 402 405 406 410 418 Theories of Column • • • • • • Chapter-15 Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers Spring • • • • • • Chapter-14 Contents Theory at a Glance (for IES, GATE, PSU) Previous 20-Years GATE Questions Previous 20-Years IES Questions Previous 20-Years IAS Questions Answers with Explanation (GATE, IES, IAS) Conventional Questions with Answers 418 422 423 428 432 438 442 442 449 450 454 456 459 469 469 473 474 476 478 480 482 482 489 490 493 495 498 504 504 506 508 510 511 513 Page-iii ________________________________________________________________________ www.iesacademy.com Email: iesacademy@yahoo.com 25, 1st Floor, Jia Sarai, Near IIT. New Delhi-16 Ph: 011-26537570, 9810958290

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1. Stress and Strain Theory at a Glance (for IES, GATE, PSU) 1.1 Stress (σ) When a material is subjected to an external force, a resisting force is set up within the component. The internal resistance force per unit area acting on a material or intensity of the forces distributed over a given section is called the stress at a point. • It uses original cross section area of the specimen and also known as engineering stress or conventional stress. Therefore, σ = • P A P is expressed in Newton (N) and A, original area, in square meters (m2), the stress σ will be expresses in N/ m2. This unit is called Pascal (Pa). • As Pascal is a small quantity, in practice, multiples of this unit is used. 1 kPa = 103 Pa = 103 N/ m2 (kPa = Kilo Pascal) 1 MPa = 106 Pa = 106 N/ m2 = 1 N/mm2 (MPa = Mega Pascal) 1 GPa = 109 Pa = 109 N/ m2 (GPa = Giga Pascal) Let us take an example: A rod 10 mm × 10 mm cross-section is carrying an axial tensile load 10 kN. In this rod the tensile stress developed is given by (σt ) = • P 10 kN 10 ×103 N = = = 100 N/mm2 = 100 MPa A (10mm × 10mm) 100 mm2 The resultant of the internal forces for an axially loaded member is normal to a section cut perpendicular to the member axis. • The force intensity on the shown section is defined as the normal stress. ΔF P σ = lim and σavg = ΔA → 0 ΔA A • Tensile stress (σt) If σ > 0 the stress is tensile. i.e. The fibres of the component tend to elongate due to the external force. A member subjected to an external force tensile P and tensile stress distribution due to the force is shown in the given figure.

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