Strength of Materials Contents - IES Academy

1 Strength of Materials Contents Sl. No. Topic Page No. Chapter - 1 Stress and Strain 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 1 1 23 27 37 45 53 Chapter - 2 Principal Stress and Strain 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 64 64 102 105 112 118 126 Chapter - 3 Moment of Inertia and Centroid 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 135 135 146 147 148 149 150 Chapter - 4 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 151 151 194 198 209 218 228 India s No 1 Strength of Materials IES Academy Contents Email.

2 _____ 25, 1st Floor, Jia Sarai, Near IIT. New Delhi-16 Ph: 011-26537570, 9810958290 Page-iiSl. No. Topic Page No. Chapter - 5 Deflection of Beam 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 240 240 277 277 281 283 286 Chapter - 6 Bending Stress in Beam 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 289 289 294 295 300 304 307 Chapter - 7 Shear Stress in Beam Theory at a glance (for IES, GATE, PSU)

3 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 313 313 317 317 320 323 326 Chapter - 8 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 327 327 332 333 334 336 Chapter - 9 Torsion 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 337 337 346 347 356 360 367 Chapter-10 Thin Cylinder 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 376 376 379 380 383 386 390 India s No 1 Strength of Materials IES Academy Contents Email: _____ 25, 1st Floor, Jia Sarai, Near IIT.

4 New Delhi-16 Ph: 011-26537570, 9810958290 Page-iiiSl. No. Topic Page No. Chapter-11 Thick Cylinder 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 393 393 402 402 405 406 410 Chapter-12 Spring 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 418 418 422 423 428 432 438 Chapter-13 Theories of Column 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)

5 Conventional Questions with Answers 442 442 449 450 454 456 459 Chapter-14 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 469 469 473 474 476 478 480 Chapter-15 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 482 482 489 490 493 495 498 Chapter-16 Riveted and Welded Joint 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 504 504 506 508 510 511 513 1.

6 Stress and Strain Theory at a glance (for IES, GATE, PSU) Stress ( ) 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, =PA P is expressed in Newton (N) and A, original area, in square meters (m2), the stress 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.

7 In this rod the tensile stress developed is given by ()() === == 32210 kN10 10 N100 N/mm100 MPa10 mm 10 mm100 mmtPA 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. == 0limandavgAFPAA Tensile stress ( t) If > 0 the stress is tensile. 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. India s No 1 Stress and Strain IES Academy Chapter-1 Email: Page-2 _____ 25, 1st Floor, Jia Sarai, Near IIT.

8 New Delhi-16 Ph: 011-26537570, 9810958290 Compressive stress ( c) If < 0 the stress is compressive. The fibres of the component tend to shorten due to the external force. A member subjected to an external compressive force P and compressive stress distribution due to the force is shown in the given figure. Shear stress ( ) When forces are transmitted from one part of a body to other, the stresses developed in a plane parallel to the applied force are the shear stress. Shear stress acts parallel to plane of interest. Forces P is applied transversely to the member AB as shown. The corresponding internal forces act in the plane of section C and are called shearing forces. The corresponding average shear stress () =AreaP Strain ( ) The displacement per unit length (dimensionless) is known as strain.

9 Tensile strain ( t) The elongation per unit length as shown in the figure is known as tensile strain. t = L/ Lo It is engineering strain or conventional strain. Here we divide the elongation to original length not actual length (Lo + L) Let us take an example: A rod 100 mm in original length. When we apply an axial tensile load 10 kN the final length of the rod after application of the load is mm. So in this rod tensile strain is developed and is given by () == == = 100 (Dimensionless) Tensile100 mm100 mmotooLLLLL India s No 1 Stress and Strain IES Academy Chapter-1 Email: Page-3 _____ 25, 1st Floor, Jia Sarai, Near IIT.

10 New Delhi-16 Ph: 011-26537570, 9810958290 Compressive strain ( c) If the applied force is compressive then the reduction of length per unit length is known as compressive strain. It is negative. Then c = ( L)/ Lo Let us take an example: A rod 100 mm in original length. When we apply an axial compressive load 10 kN the final length of the rod after application of the load is 99 mm. So in this rod a compressive strain is developed and is given by () == == = 99 mm 100 (Dimensionless) compressive100 mm100 mmocooLLLLL Shear Strain ( ): When a force P is applied tangentially to the element shown. Its edge displaced to dotted line. Where is the lateral displacement of the upper face of the element relative to the lower face and L is the distance between these faces.