Wednesday, 19 May 2021

Multiple Choice Questions and Answers (Structural Engineering)









Structural Mechanics

1. Portal frames are frequently used in a building to:

A. Transfer vertical forces

B. Transfer moment

C. Transfer horizontal forces

D. It is a zero it is used to transfer horizontal force applied at top of frame to foundation

Answer: C

2. Which of the following supports are not used in portals?

A. Fixed

B. Pin

C. partial

D. Roller

Answer: D

3. Where point of inflection located in top girder in a pin supported portal frame?

A. At one of the ends

B. At both ends

C. At center of beam

D. Inflection point is not present

Answer: C

4. What is the degree of indeterminacy of a fixed supported portal frames?

A. 1

B. 2

C. 3

D. 4

Answer: C

5. What is the relation between shear at the base of each columns of a portal frame which is fixed supported (given length of columns are equal)?

A. They are equal

B. One is double of other

C. One is triple of other

D. Depends upon magnitude of load applied

Answer: A

6. Cantilever method is based upon same action as a long cantilever beam subjected to a

A. Transverse load

B. Axial load

C. Moment

D. No load

Answer: A

7. Where does neutral axis of column lie?

A. Vertical plane

B. Horizontal plane

C. Both of them

D. Neither of them

Answer: B

8. In Gaussian elimination method, original equations are transformed by using _____________

A. Column operations

B. Row Operations

C. Mathematical Operations

D. Subset Operation

Answer: B

9. Which of the following step is not involved in Gauss Elimination Method?

A. Elimination of unknowns

B. Reduction to an upper triangular system

C. Finding unknowns by back substitution

D. Evaluation of cofactors

Answer: D

10. Solve the equations using Gauss Jordan method.

x + 2y + 6z = 22

3x + 4y + z = 26

6x - y - z = 19

A. x = 4, y = 3, z = 2

B. x = 3, y = 4, z = 2

C. x = 3, y = 2, z = 4

D. x = 4, y = 6, z = 2

Answer: D

11. Which of the following methods is used for obtaining the inverse of matrix?

A. Gauss Seidel method

B. Newton Raphson method

C. Gauss Jordan method

D. Secant Method

Answer: C

12. If in planar system, X parts/members are there with Y no. of forces, then condition for statically determinacy is

A. Y < 3X

B. Y > 3X

C. Y = 3X

D. None of the mentioned

Answer: C

13. If 4 reactions are acting on a beam, then the system is

A. Unstable & indeterminate

B. Stable & indeterminate

C. Stable & determinate

D. Can’t say

Answer: D

14 The number of equilibrium equations for the following space frame is ____

A. 1

B. 3

C. 6

D. 4

Answer: C

15. External Static Indeterminacy of the following beam is _______

A. 2

B. 4

C. 3

D. 0

Answer: B

16. What is kinematic indeterminacy for the given figure without considering axial deformation?

A. 0

B. 2

C. 4

D. 6

Answer: B

17. Approximate analysis is done on a

A. Determinate structures

B. Indeterminate structures

C. Determinate and indeterminate structures

D. Depends upon load applied

Answer: A

18. Points of inflection can be considered as

A. Pin support

B. Roller support

C. Link support

D. Pin

Answer: D

19. Who of the following initially developed force method?

A. Muller

B. Breslau

C. Mohr

D. James clerk Maxwell

Answer: D

20. Flexibility coefficients are used in which of the following method?

A. force method

B. displacement method

C. both force and displacement method

D. virtual force method

Answer: A

21. Which of the following is the correct equation for Degree of Static Indeterminacy of a truss?

A. (m+r) -2j

B. (m+r) + 2j

C. (m-r)-2j

D. (m-r) +2j

Answer: A

22. Stiffness of the end A if the far end B is fixed is ____

A. EI/L

B. 2EI/L

C. 3EI/L

D. 4EI/L

Answer: D

23. In displacement method of structural analysis, the basic unknowns are

A. displacements

B. force

C. Displacements and forces

D. None of the above

Answer: A

24. The deformation of spring caused by unit load is called as

A. stiffness

B. flexibility

C. Influence coefficient

D. Unit strain

Answer: B

25. The kinematic indeterminacy of the plane truss shown in the figure is

A. 11

B. 8

C. 3

D. 0

Answer: A

26. Find determinant of the following matrix [3 4 1; 0 -1 2; 5 -2 6]

A. 19

B. 29

C. 39

D. 49

Answer: C

27. Transpose of Matrix A  [1 5 7 8 ] is said to be

A. Column matrix

B. Row matrix

C. Square matrix

D. Identity matrix

Answer: A

28. The stiffness matrix of a beam element is given as


A. a

B. b

C. c

D. d

Answer: C

29. For the beam shown below, the stiffness coefficient K22 can be written as

A. 6EI/L2

B. 12EI/L3

C. 3EI/L

D. EI/6L3

Answer: B

30. The stiffness coefficient Kij indicates

A. Force at i due to unit deformation at j

B. Deformation at j due to unit force at i

C. Deformation at i due to unit force at j

D. Force at j due to unit deformation at i

Answer: A

31. If in a pin-jointed plane frame (m + r) > 2j, then the frame is

A. Stable and statically determinate

B. Stable and statically indeterminate

C. Unstable

D. None of the above

Answer: B

32. Principle of superposition is applicable when

A. Deflections are linear functions of applied forces

B. Material obeys Hooke’s law

C. The action of applied forces will be affected by small deformations of the structure

D. None of the above

Answer: A

33. The Castigliano’s second theorem can be used to compute deflections

A. In statically determinate structures only

B. For any type of structure

C. At the point under the load only

D. For beams and frames only

Answer: B

34. For stable structures, one of the important properties of flexibility and stiffness matrices is that the elements on the main diagonal

1. of a stiffness matrix must be positive

2. of a stiffness matrix must be negative

3. of a flexibility matrix must be positive

4. of a flexibility matrix must be negative

(1) and (3)

(2) and (3)

(1) and (4)

(2) and (4)

Answer: A

35. Which of the following methods of structural analysis is a force method?

A. Slope deflection method

B. Column analogy method

C. Moment distribution method

D. None of the above

Answer: B

36. Which of the following methods of structural analysis is a force method?

A. Slope deflection method

B. Column analogy method

C. Moment distribution method

D. None of the above

Answer: B

37. Which of the following is not the displacement method?

A. Equilibrium method

B. Column analogy method

C. Moment distribution method

D. Kani’s method

Answer: B

38. If in a rigid-jointed space frame, (6m + r) < 6j, then the frame is

A. Unstable

B. Stable and statically determinate

C. Stable and statically indeterminate

D. None of the above

Answer: A

39. To generate the jth column of the flexibility matrix

A. A unit force is applied at coordinate j and the displacements are calculated at all coordinates

B. A unit displacement is applied at coordinate j and the forces are calculated at all coordinates

C. A unit force is applied at coordinate j and the forces are calculated at all coordinates

D. None of the above

Answer: A

40. In the displacement method of structural analysis, the basic unknowns are

A. Displacements

B. Force

C. Displacements and forces

D. None of the above

Answer: A

41. A rigid-jointed plane frame is stable and statically determinate if; (Where m is number of members, r is reaction components and j is number of joints)

A. (m + r) = 2j

B. (m + r) = 3j

C. (3m + r) = 3j

D. (m + 3r) = 3j

Answer: C

42. Degree of kinematic indeterminacy of a pin-jointed plane frame is given by

A. 2j – r

B. j – 2r

C. 3j – r

D. 2j + r

Answer: A

43. The number of independent equations to be satisfied for static equilibrium of a plane structure is

A. 1

B. 2

C. 3

D. 6

Answer: C

44. Select the correct statement

A. Flexibility matrix is a square symmetrical matrix

B. Stiffness matrix is a square symmetrical matrix

C. Both (A) and (B)

D. None of the above

Answer: C

45. Study the following statements.

(i) The displacement method is more useful when degree of kinematic indeterminacy is greater than the degree of static indeterminacy.

(ii) The displacement method is more useful when degree of kinematic indeterminacy is less than the degree of static indeterminacy.

(iii) The force method is more useful when degree of static indeterminacy is greater than the degree of kinematic indeterminacy.

(iv) The force method is more useful when degree of static indeterminacy is less than the degree of kinematic indeterminacy.

The correct answer is

A. (i) and (iii)

B. (ii) and (iii)

C. (i) and (iv)

D. (ii) and (iv)

Answer: D

46. The number of independent displacement components at each joint of a rigid-jointed space frame is

A. Three linear movements

B. Two linear movements and one rotation

C. One linear movement and two rotations

D. Three rotations

Answer: B

47. Degree of static indeterminacy of a rigid-jointed plane frame having 15 members, 3 reaction components and 14 joints is

A. 2

B. 3

C. 6

D. 8

Answer: C

48. The deformation of a spring produced by a unit load is called

A. Stiffness

B. Flexibility

C. Influence coefficient

D. Unit strain

Answer: B

49. How many constraints are there in a fixed support?

A. 2

B. 3

C. 6

D. Can’t say

Answer: D

50. Moment at a hinge will be

A. Infinity

B. Zero

C. Depends upon acting forces

D. None of the above

Answer: B

51. A surface structure has

A. Small thickness

B. Large thickness

C. Moderate thickness

D. Arbit thickness

Answer: A

52. For the validity of principle of superposition, materials should behave in which manner?

A. linear-elastic

B. non-linear-elastic

C. Non-linear- inelastic

D. Linear- inelastic

Answer: A

53. A roller support is shown in figure identify the true free body diagram


A. i

B. ii

C. iii

D. iv

Answer: B

References

https://www.examveda.com/

https://www.sanfoundry.com/

https://www.indiabix.com/




Wednesday, 5 May 2021

Finite Element Method/ Finite Element Analysis

Disclaimer:

This document does not claim any originality and cannot be used as a substitute for prescribed textbooks. I would like to acknowledge various sources like freely available materials from the internet particularly NPTEL/ SWAYAM course material from which the lecture note was prepared. The ownership of the information lies with the respective authors or institutions. Further, this document is not intended to be used for commercial purposes and the BlogSpot owner is not accountable for any issues, legal or otherwise, arising out of the use of this document.

This open resource is a collection of the academic courses of under graduation program for B. Tech (Civil Engineering) and M. Tech as per the syllabus of  Dr. B.A.T University, Lonere, Raigad (m.s), India prepared by Dr. Mohd. Zameeruddin,  Associate Professor, MGM's College of Engineering, Nanded for use in the out-of-class activity. The content covers both theoretical and analytical studies. There are six lessons as part of this document and each deals with an aspect related to Finite Element Analysis and Finite Element Method.

Module 1: Introduction to FEM & Approximate Methods

Module 2: One Dimensional FE Analysis

Module 3: FE Analysis by Direct Approach

Module 4: Two Dimensional FE Analysis

Module 5: Three Dimensional FE Analysis

Module 6: Computer Implementation of FEM

Module 1: Introduction to FEM & Approximate Methods

The finite element method (FEM) is a numerical analysis technique for obtaining approximate solutions to a wide variety of engineering problems [Vishal Jagota et al., 2013]. In this method, all the complexities of problems like varying shape, boundary conditions, and loads are maintained as they are but the solution's obtained are approximate. Because of its diversity and flexibility as an analysis tool, it is receiving much attention in engineering. A number of the popular brands of finite element analysis packages are now available commercially, for example, STAAD PRO, NASTRAN, NISA, and ANSYS.  

    In engineering problems. there are some basic unknowns. If they are found, the behavior of the entire structure can be predicted. The basic unknowns or the field variables which are encountered in the engineering problems are displacements in solid mechanics, velocities in fluid mechanics, electric and magnetic potentials in electrical engineering, and temperatures in heat flow problems. 

     In a continuum, these unknowns are infinite. The finite element procedure reduced such unknowns to a finite number by dividing the solution region into small parts called elements and by expressing the field variables in terms of assumed approximating function within each element. The approximating functions are defined in terms of field variables of a specified point called nodes or nodal points. Thus in finite element analysis, the unknowns are field variables at any point that can be found by interpolation functions.

 After selecting elements and nodal unknown next step in finite element analysis is to assemble element properties for each element. Thus the various steps involved in the finite element analysis are;

1. Select suitable field variables and the elements 

2. Discretize the continua

3. Select the interpolation functions

4. Find the element properties

5. Assemble element properties to get global properties

6. Impose the boundary conditions 

7. Solve the system equations to get the nodal unknowns

8. Make the additional calculations to get the nodal unknowns

The finite element knowledge makes a good engineer better while just user without the knowledge of FEA may produce more dangerous results. To use FEA packages properly the user must know the following points clearly;

1. Which element are to be used for solving problem in hand

2. How to discretize to get good results

3. How to introduce boundary conditions properly

4. How the element properties are developed and what are their limitations

5. To check the ability of available software

 Flowchart [Step-wise procedure of finite element analysis]

Continuum – Discretization of continuum in finite element – Selection of displacement function – Derivation of element stiffness matrix – Assembly of algebraic equation for the overall discrete continuum – Solution for the unknown displacement – Computation of element stress and strain from the nodal displacement

Question: Discuss in step by step finite element process and draw a flow chart for the same

Merits and Demerits of Finite Element Analysis/ Finite Element Method

Compared to other numerical finite element analysis merits are as follows;

1. The modelling of a complex geometries and irregular shapes are made easier by using finite element method.

2. Boundary conditions can be easily incorporated in finite element method.

3. Different types of material properties can be easily assigned in modelling from element to element or within an element.

4. Problems with heterogeneity, anisotropy, non-linearity and time-dependency can be easily dealt with finite element method.

5. The systematic procedure of finite element method makes it a powerful and versatile tool for a wide range of problems. 

6. Finite element method is simple, compact and result oriented and widely popular among engineering community. 

7. Finite element method can be easily coupled with computer aided design (CAD) programs in various disciplines in engineering. 

8. In finite element method it’s relatively easy to control the accuracy by refining the mesh or using higher order elements.

Demerits

1. Closed-form expressions in terms of problem parameters are not available in finite element method.

2. Numerical solution is obtained at only once for a specific problem case.

3. Large amount of data requires as input for mesh

4. Generally, voluminous (lengthy) output data must be analysed and interpreted.

5. Experience, good engineering judgment and understanding of the physical problems are required.

6. Poor selection of element types or discretization may lead to faulty results.

Question:  Explain briefly merits and demerits of finite element method

Application of finite element method


     

 

 

 

Reference Books:

1.     Finite Element Method by S. S. Bhavikati 

2. Finite Element Method with Application inn Engineering by Y. M. Desai, T. I. Eldhoand A.H.Shah