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Applied Mechanics Tutorials -2

Diploma in Civil Engineering

Applied Mechanics

Tutorials -2

A block of mass M = 10 kg is sitting on a surface inclined at angle θ = 45°. Given that the coefficient of static friction is μs = 0.5 between block and surface, what is the minimum force F necessary to prevent slipping? What is the maximum force F that can be exerted without causing the block to slip? 

ANS: Fmin = 34.65 N, Fmax = 103.94 N 


In the previous problem use θ = 15°. What is the maximum force pushing down the incline so that the block doesn't slip? What is the maximum force pushing up the incline so that the block doesn't slip? 
Answer: Fmax = 21.97 N (pushing down the incline), Fmax = 72.69 N (pushing up the incline) 


A block weighing 80 N rests on a plane inclined at 30 degrees to the horizontal. The coefficients of static and kinetic friction are 0.2 and 0.1 respectively. What is the minimum magnitude of the force F, parallel to the plane, that will prevent the block from slipping?
Answer: F= 26N


A car (m=2000 kg) is parked on a road that rises 20 degrees above the horizontal. What are the magnitudes of (1) the normal force and (2) the static frictional force that the ground exerts on the tires?
 Answer :normal force:1.8x10^4N static friction force:6.7x10^3N

Important Topic

Friction and Laws of Static friction

Limiting Friction

Angle of Friction Coefficient of Friction

Syllabus For Applied Mechanics(CTEVT)

Applied Mechanics 

EG 2102 CE

 Year: II Semester: I 

 Total: 6 hours /week

 Lecture: 3 hours/week Tutorial: 2 hours/week 

 Practical: hours/week Lab: 2/2 hours/week 

 Course description: This course focuses on analysis and effect of various types of forces on the particle and body at rest. Course objectives: After the completion of this course, students will be able to: 

1. Understand the concept of particle and rigid body and application of equations of static equilibrium; 

2. Describe the different types of forces that may act on the body and analysis of typical problems; 

3. Be familiar with the frictional force on the body and analysis of typical problems; 

4. Be familiar with the distributed forces (Centre of gravity, Centroid, and Moment of Inertia) and calculation and 

5. Know about the structure (beam and truss), their supports, loads and analysis of them. 

 Course Contents: 

Theory 

Unit 1 Introduction: [4 Hours] 

1.1 Definition and scope of Applied Mechanics 

1.2 Concept of Particle, Rigid Body, Deformed Body, Free Body Diagram and Equilibrium of particle and Rigid Body 

1.3 Equations of Static Equilibrium: Two and Three Dimensional analysis of Particle, Two Dimensional analysis of Rigid Body 

Unit 2 Forces acting on Particle and Rigid Body: [9 Hours] 

 2.1 Different types Forces: Internal, External, Translational, Rotational, Coplanar, Non-Coplanar, Concurrent, Non-Concurrent, Like Parallel and Unlike Parallel 

 2.2 Resolution and Composition of Forces 

 2.3 Principle of Transmissibility and Equivalent Forces 

 2.4 Moments and Couples 

 2.5 Varignon’s Theorem 

 2.6 Resolution of a Force in to a Force and a Couple 

 2.7 State and Prove: Triangle Law of Forces, Parallelogram law of Forces Polygon Law of Forces and Lami’s Theorem  

Unit 3 Friction: [5 Hours] 

 3.1 Friction: Definition, Causes, Advantages, Disadvantages and Types 

 3.2 Laws of Dry Friction 

 3.3 Static and Dynamic Friction and Their Coefficients 

 3.4 Angle of Friction 

3.5 Different status (No Friction, Certain Friction, Impending Motion and Motion) 

 3.6 Sliding and Tipping Condition of the Body 

Unit 4 Centre of Gravity and Centroid: [6 Hours] 

 4.1 Concept of Centre of Gravity, Centroid, Axis of Symmetry 

 4.2 Centroid of Composite lines (straight line, arc, semicircle and quarter circle) 

 4.3 Centroid of Composite Area (Rectangle, Triangle, Circle / Semi-circle / Quarter circle / Circular sector, Parabola / Semi-parabola and Ellipse) 

 4.4 Centroid of Area under curve by the method of Integration 

Unit 5 Moment of Inertia: [6 Hours] 

 5.1 First Moment and Second Moment of Area 

 5.2 Axial and Polar Moment of Inertia 

 5.3 Moment of Inertia of Regular Areas (Rectangle, Triangle, Circle and Ellipse) about their Centroidal axes 

 5.4 Perpendicular and Parallel axis Theorem for Moment of Inertia 

 5.5 Moment of Inertia of Composite Area 

 5.6 Radius of Gyration 

Unit 6 Structures: [5 Hours] 

 6.1 Structure and Mechanism 

 6.2 Plane and Space Structures 

 6.3 Different types of Load and Support in the Structures 

 6.4 External and Internal forces (Axial Force, Shear Force, and Bending Moment) in the Structural Members 

 6.5 Relationship between Load, Shear Force and Bending Moment 

 6.6 Determinacy and Stability (Statically and Geometrically) of the Structures 

Unit 7 Analysis of Statically Determinate Beam: [5 Hours] 

 7.1 Definition and Types of Beam 

 7.2 Calculation of Support Reactions and Internal Forces (i.e. Axial Force, Shear Force and Bending Moment) of the Beam  

7.3 Draw Axial Force, Shear Force and Bending Moment Diagrams of the Beam 

Unit 8 Analysis of Statically Determinate Plane Truss : [5 Hours] 

 8.1 Definition, uses and Types of Truss 

 8.2 Calculation of Member Force by the Method of Joints 

 8.3 Calculation of Member Force by the Method of Sections  

Practical (Laboratory) [15 Hours] 

1. Verify Triangle law of forces, Parallelogram law of forces and Lami’s theorem 

2. Verify Principle of Moments 

3. Determine Centroid of Plane Figures (Rectangle, Triangles, Circle and Ellipse) 

4. Determine Moment of Inertia by Flywheel 

5. Determine Support Reactions of Simply Supported and Cantilever Beam with different types of Loading 

6. Determine Support Reactions and Member Force of Simply supported Truss 

Applied Mechanics Tutorials

Diploma in Civil Engineering

Applied Mechanics

Tutorials -1

Following force are acting on a particle

a) Roll No KN at Roll no⁰ to the Horizontal,

b) 8KN at 90⁰ to the horizontal,

c) 45 KN at 200⁰ to the horizontal,

d) 35KN at 320⁰ to the horizontal

ANS: Roll NO 1:R=33.15@244.17,Roll No 47:R=17.16@195.19(Resultant and Angle are Decrease with increasing Roll no)

Following force are acting on a particle

a) 25KN at Roll no⁰ towards  north of east

b) 30KN at towards to north

c) 45 KN at 45⁰ towards north of west

d) 35KN at 30⁰ towards south of west

ANS: Roll NO 1:R=74.7@130.88,Roll No 47:R=57.60@122.6(Resultant and Angle are Decrease with increasing Roll no)

Find out the magnitude and direction of following system

              

ANS: Roll NO 5:R=42.9@115.69,Roll No 40:R=94.26@267.32(Resultant and Angle are Increase with increasing Roll no)

Find out the magnitude and direction of following system

               

ANS: Roll NO 12:R=179.04@2.69,Roll No 38:R=162.88@371.17

If System is in Equilibrium find the unknown force

               

ANS: R=10

Determine the Direction of force F So that resultant of the force is horizontal. Find The Resultant Also.

If force a)F=1700KN    b) F=2500KN   c) F=3000KN                                                                                            

Ans a)289.77⁰ R=1265.70004      b)320.21⁰ R=2612.8012       c)327.77 R=3227.80015

Find the resultant and Distance of resultant from O and Moment at

Ans R=800KN, Distance from O=5.33m M=4800KNM

Find the resultant and Distance of resultant from O and Moment at O.

Ans R=3256KN, Distance from O=4.25m Angle of Resultant=61⁰48’00”

Two loads of 30 N and WF are hung by a set of wire ropes as shown in figure. Determine the tensions in the wire ropes AB, BC and CD. Also determine the unknown weight WF hung at the point B.

Ans  TCB = 100.38 N, TCD = 111.96 N, TBA = 137.12 N, WF = 122.94 N

A smooth sphere of diameter 20 cm weighing 20 N is supported by a string fixed to the wall. The length of the string is three times the radius of the sphere. Determine the reaction at the wall and the tension in the string.

Ans The tension in the string, T = 21.21 N

Reaction exerted by the wall, R = 7.07 N

Important Topic

Parallelogram Law of Force

Couple and Characteristics

Lami’s Theorem

Resultant of Force

Like/Unlike Parallel force

Equilibrium and Condition of Equilibrium

Moment

Varignon’s theory

Triangle Law, Polygon Law

Free body Diagram

Coplanar, non Coplanar Force  

SIMPLE GATE DESIGN DRAWING

GUIDELINES ON STORING OF CEMENT ON SITE

In large work or in major construction works, cement is generally stored at site. The cement must be stored in such a manner so that, it can be easily accessible for proper inspection. The building in which cement is stored should be water tight in order to prevent dampness.

The guidelines given below should be observed while storing the cement.

1.      Cement should not be stored for a long period. During rainy season, the storage time period of cement should be as minimal as possible.

2.      Dampness in godowns must be avoided.

3.      Cement should not be piled against the wall. A minimum space of 30 cm all –round should be left between the exterior walls and the tacks. The distance between two consecutive stacks should be the minimum to reduce circulation of air.

4.      Cement should not be piled directly on the floor; instead it should be piled off the floor on wooden planks so as to be clear of the floor by at least 10 to 20 cm.

5.      There should not be more than 15 bags in one pile. This is done to avoid lumping under pressure.

6.      Cement bags should be arranged that they can be used on the principle of “first come first served”.

7.      If more than 7 bags of cement are to be stored in a pile, then it can be arranged in header and stretcher fashion or alternatively lengthwise and crosswise so as to tie the piles together and to avoid the danger of toppling over.

8.      When cement bags is to be stored for a long period or during rainy season, the stack should be enclosed completely by polythene sheet, tarpaulin or any other suitable water proofing material.

9.      If different brands of cement are meant to be used on one work, they should be stacked separately.

©Ishu Mainali