MARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter. Applications of. Friction. Centroid & Moment.

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1 Introduction Fundamentals of statics Applications of fundamentals of statics Friction Centroid & Moment of inertia Simple Stresses & Strain Stresses in Beam Torsion Principle Stresses DEPARTMENT OF CIVIL ENGINEERING BRANCH : Civil Engineering DISPLAY DATE : BATCH : 3 rd Bx, By, Bz SUBMISSION DATE : Instructions: 1) Every student has to complete assignments and get it checked by respective lab teacher on or before due date given by lab teacher. 2) During each lecture, student should write important points of the lecture (such as brief notes, equations, sketches, etc. Many lectures have numerical which may be partially solved in the class those problems should be completed before the next class. Sometimes, additional problems will be given during the class and those also should be completed before the next lecture. 3) If you miss the lectures for medical reason, submit the doctor certificate to Head of department and keep the zerox with you till the end of the course. 4) The lecture notes will be randomly evaluated by Teacher without any prior notice. 5) Student should start writing tutorial with keeping first page question set zerox sheet in file. MARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter Paper Year Dec Jun Dec Jun Avg Darshan Institute Of Engineering & Technology Page 1/8

2 Module I Chapter-1 Introduction Q-1 Fill in th`e blanks with the most appropriate answer 1) A body is said to be in equilibrium if it has no linear motion (True, False ) 2) 10 6 kg = [10 3, 10-6, 10 9, 10-3 ] Mg. 3) A mild steel bar under tension test shows property of [malleability, ductility, tensionability] 4) Mass is a quantity. a) Vector b) Scalar c)tensor 5) Law of Parallelogram of forces is applicable to forces. a) Two Parallel b) Two concurrent c) Three Parallel 6) Splitting of force in given directions is known as of force. (resolution, composition, division) 7) Moment is a vector, whereas Couple is a vector. (free, null, fixed) 8) is equal and opposite to the resultant of several forces acting on a body. (Equilibrant, Resultant, Stress, Strain) 9) The process of finding components of a force is called of forces. (Desolution, Resolution, Lami s theorem, Composition) Q-2 Answer in one line 1) Resultant of two forces can be found using which law? 2) Force is defined by its magnitude and other parameters. Name them. Q-3 Define the following terms: (a) Statics (b) Dynamics (c) Kinetics (d) Kinematics (e) Rigid body (f) Deformable body (g) Particles Q-4 What do you understand by mechanics? Enlist the fundamental principles of mechanics and explain them. Q-5 Differentiate between Scalar and Vector quantity. Write S.I. units of following quantities and categorize it as a scalar or vector. Density 2. Velocity 3. Volume 4. Momentum 5. Work Q-6 Convert following S.I. units to the unit indicated. 150 MPa to kn/mm2 2) 10 6 kg to Mg 3) 40 Mg to kn 4) 20kNm to Joule Darshan Institute Of Engineering & Technology Page 2/8

3 Chapter-2 Fundamental of Statics 1) If arm of couple is doubled, its moment will ( be halved, Remain the same, be Doubled ) 2) Three coplanar non-parallel forces in equilibrium will [always, never, sometimes] be concurrent. 3) Two forces under equilibrium must be ( non rectilinear, rectilinear, parallel) 4) is a scalar quantity.( momentum, force, work) 5) 100 mm = μm ( 10 5, 10 6, 10-7 ) 6) of a force is the procedure of splitting a force into number of components 7) is equal and opposite to the resultant of several forces, acting on a body. 8) Three coplanar non-parallel forces in equilibrium will be concurrent. [always, never, sometimes] 9) Two equal and opposite parallel forces, whose lines of action are not same, form a. a) Shear Force b) Couple c) Principal Stress Q-2 Define Force. What are the characteristics and types of forces? Explain briefly. Q-3 State and prove Lami s theorem. Q-4 State the law of parallelogram of forces. Q-5 Determine magnitude and direction of resultant force of the force system shown in fig. 1 Q-6 A system of connected flexible cables shown in fig. 2 is supporting two vertical forces 130N and 170N at point A and B. Determine the forces in various segments of the cables. Q-7 Find magnitude, direction and location of resultant of force system with respect to point A shown in fig. 3. Q-8 State and prove Varignon s principle of moment. Figure 3 Darshan Institute Of Engineering & Technology Page 3/8

4 Module II Chapter-3 Applications of fundaments of statics 1) In a cantilever, carrying a load whose intensity varies uniformly from zero at the free end to w per unit run at the fixed end, the S.F diagram changes following a ( Linear law, Parabolic law, cubic law ) 2) The shape of shear force diagram for cantilever beam subjected to couple at free end is [horizontal straight line, zero, parabola, incline straight line]. 3) Point of contra flexure is where [shear force is zero, shear force changes sign, bending moment changing sign, bending moment is zero] 4) Beam extends beyond the support then that beam is known as beam. 5) At free end of a cantilever bending moment is always unless a concentrated moment is applied at the free end 6) A Hinge support offers support reactions. a) One b) Three c) Two 7) Bending moment is at a hinged support. (always maximum, always zero) 8) Statically determinate structures can be analysed using the 3 equations of 9) The relationship between Shear force (V) and Bending moment (M) is given by the differential 10) The shape of shear force diagram for cantilever beam subjected to couple at free end is [horizontal straight line, zero, parabola, incline straight line]. 11) At the point of contraflexure changes its sign. (shear force, bending moment, axial force) Q-2 Discuss the various types of supports, beams, and load acting on the beam with symbolic sketches Q-3 Derive the relation between loading intensity, shear force and bending moment with usual notation Q-4 Find the reactions at supports for a beam loaded as shown in fig. 1. Q-5 Draws shear force and bending moment diagrams for beam shown in fig. 2. Giving values at all important points Darshan Institute Of Engineering & Technology Page 4/8

5 Module III Chapter-4 Friction 1) If a ladder is not in equilibrium against a smooth vertical wall, than it can be made in equilibrium by ( Increasing angle of inclination with vertical, Increasing angle of inclination with horizontal, Increasing the length of ladder) 2) Coefficient of static fiction is [less than, more than, equal to] coefficient of dynamics fiction. 3) True relation between dynamic coefficient of friction (μd) and static coefficient of friction ( μs ) is ( μd > μs, μd = μs, μd < μs ) 4) Force of friction is to the applied force, which tends to move the body. 5) When a block is on the verge of sliding down the inclined plane, Friction is. a) Minimum b) Maximum c) Zero 6) Angle of repose is equal to angle of static friction when. (motion is absent, system is in equilibrium, motion is impending, body is on a flat surface) Q-2 Define Friction, Coefficient of friction and angle of repose. Q-3 A ladder 7 m long rests against a vertical wall with which it makes an angle of 45º and resting on a floor. If a man whose weight is one half of that the ladder, climbs it. At what distance along the ladder will he be when ladder is about to slip? μ= 1/3 at wall and 1/2 at floor Chapter-5 Centroid and moment of inertia 1) Moment of inertia of any plane area is maximum about an axis passing though. Q-2 State and prove parallel and perpendicular axis theorem with usual notations. Q-3 State Pappus Guldinus Theorem for volume of solid and surface of revolution. Q-4 Determine co ordinates of centroid with respect to O of the section shown in fig.1 Q-5 Determine moment of inertia of a section shown in fig. 2 about horizontal centroidal axis Darshan Institute Of Engineering & Technology Page 5/8

6 Module IV Chapter-6 Simple stresses and strains 1) Which one of expressions is NOT true [E = 2G(1+μ), E = 3K(1-2μ), E = 9KG/(3G+K), M = σ.i/y]. 2) Lateral strains are longitudinal strains. (always less than, sometimes less than, never less than) 3) As per Hooke's law, Within elastic limit, Stress is proportional to Strain. a) Directly b) Inversely c) Not 4) Lateral Strain and Linear Strain are of nature. a) Same b) Opposite 5) Poisson s ratio is ratio of (longitudinal to lateral strain, lateral to longitudinal strain, shear stress to shear strain) 6) Forces acting transverse to the axis of the member will produce stress 7) The is found from the stress vs strain relation of a material. 8) The constant of proportionality for a member under shear stress and strain is given by the Modulus of 9) Lateral strains are longitudinal strains. (sometimes less than, always less than, never less than) 10) Relation between Modulus of Elasticity and Bulk Modulus is. Q-2 Answer in one line 1) The Elastic Range is defined by which Law? 2) Name the various elastic constants and give their relationship Q-3 Define following terms. 1-Linear strain, 2-Poisson s ratio, 3-Lateral strain, 4-Shear Stress, 5-Tensile stress, 6-Modulus of Rigidity, 7-Compressive stress, 8-Modulus of Elasticity, 9- Thermal stress Q-4 Calculate the force P required for equilibrium of bar shown in Fig. 1 Determine total change in length of the bar. Es= 200 GPa, Eb=100Gpa, Ea=75 Gpa Q-5 An assembly made up from aluminum and steel bars as shown in fig. 2 is initially stress free at temperature 32 0 C. The assembly is heated to bring its temperature to 82 0 C. Find the stress developed in each bar. The coefficient of thermal expansion is 1.25x10-5 / 0 C and 2.25x10-5 / 0 C for steel and aluminum respectively. Take E s =200Gpa and E al =75Gpa Darshan Institute Of Engineering & Technology Page 6/8

7 Module V Chapter-7 Stresses in Beams 1) Strength of the beam is mainly depend upon ( c.g of the section, its weight, section modulus ) 2) The ratio of the maximum shear stress to average shear stress is for 4/3, the cross section would be [triangular, rectangular, circular, hexagonal]. 3) The Bending or Flexural equation is given by: = = 4) Ratio of maximum to average shear stress in a rectangular section is. (3/2, 1/2, 3/4, 5/2) 5) One of the assumption in theory of pure bending is the value of is same in tension as well as compression. (Moment of Inertia, Modulus of Elasticity, Shear Stress, Bending Stress) Q-2 Derive equation of bending stress Q-3 Derive equation of shear stress Q-4 Sketch shear stress and bending stress distribution diagrams for (i) Rectangular section (ii) Circular section(iii) T section (iv) I section (v) Triangular section Q-5 Determine the bending stress distribution for the beam shown in fig.e 1. If thecross section of the beam is 230mm X450mm. Sketch the bending stressdiagram Q-6 Determine the maximum shear stress and draw shear stress distribution Across the section as shown in fig. 2,if the section is subjected to a sheerforce of 40kN Chapter-8 Torsion 1) Twisting of an object due to applied torque is known as (Bending, Shearing, Torsion, Rotation) Q-2 Derive generalized formula for torsion of circular shaft (with usual notation) Q-3 Determine the diameter of a solid shaft which will transmit 300 kw at 250 r.p.m. The maximum shear stress should not exceed 30 N/mm 2 and twist should not be more than 1 in a shaft length of 2 m. Take modulus of rigidity = 10 5 N/mm 2. Q-4 A hollow shaft has to transmit 300kW power at 80 rpm. If the shear stress is not to exceed Darshan Institute Of Engineering & Technology Page 7/8

8 60 N/mm 2 and internal diameter is 60% of the external diameter, find the external and internal diameters when maximum torque is 1.4 times the average torque. G= 8 x 10 4 N/mm 2 Q-5 A solid steel shaft has to transmit 350 kw at 900 r.p.m. Find the diameter of the shaft if the shear stress is to be limited to 125 N/mm 2. Calculate the diameter of the shaft Chapter-9 Principle Stresses 1) The difference of angle between two principal plane is (180, 90,120,45 ) Q-2 What are principal planes and principal stresses? Q-3 At a point in a strained material, stress conditions on two planes; making an angle of 60º between two, are as shown in fig. 1. Determine the principal planes and principal stresses through the point. Q-4 An element is loaded by tensile stress 5MPa and compressive stress 4MPa in perpendicular directions along with shear stress 3MPa as shown in fig 2. Calculate normal, tangential and resultant stress on a plane making 300 angle in anticlockwise direction with the plane carrying tensile stress Darshan Institute Of Engineering & Technology Page 8/8

SN QUESTION YEAR MARK 1. State and prove the relationship between shearing stress and rate of change of bending moment at a section in a loaded beam.

SN QUESTION YEAR MARK 1. State and prove the relationship between shearing stress and rate of change of bending moment at a section in a loaded beam. ALPHA COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING MECHANICS OF SOLIDS (21000) ASSIGNMENT 1 SIMPLE STRESSES AND STRAINS SN QUESTION YEAR MARK 1 State and prove the relationship