How to prepare SOM and Structural Analysis for GATE Civil Engineering
This article on SOM and Structural Analysis has been written by Rohit Sachdeva. He graduated from Delhi College of Engineering (now DTU) in 2012 (a gold medalist in his batch) in Civil Engineering branch. Then he appeared in Civil Engineering (CE) paper in GATE 2017 and secured an All India Rank (AIR) of 93.
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In this blog, I will be discussing how to prepare 2 major and most difficult considered subjects in Civil Engineering: Strength of Materials (SOM) and Structural Analysis. Not only do these topics carry a lot of weightage in GATE, they are favorites for interviewers in both PSUs and IITs. Anyone considering to pursue career as a Structural Engineer will encounter most of these concepts throughout his/her life. Considered to be the backbone of Civil Engineering, Structures is also the most sought after branch in M.Tech as well as, as a career option in India.
A rough breakup of questions of various topics in last 30 years in GATE is as follows:
Sl No | Topic | No. of Questions | |
1 mark | 2 marks | ||
STRENGTH OF MATERIALS | |||
1 | Properties of Material, Simple Stress-Strain & Elastic Constants | 11 | 9 |
2 | SFD and BMD | 4 | 12 |
3 | Principal Stress-Strain & Theories of Failure | 10 | 8 |
4 | Bending Stresses in Beams | 3 | 5 |
5 | Shear Stresses in Beams | 5 | 4 |
6 | Slope & Deflection of Beams | 1 | 24 |
7 | Thick & Thin Cylinders and Spheres | 3 | 1 |
8 | Torsion in Shafts & Springs | 1 | 7 |
9 | Theory of Columns | 8 | 8 |
10 | Centroid, Moment of Inertia & Shear Centre | 2 | 2 |
STRUCTURAL ANALYSIS | |||
11 | Determinacy/Indeterminacy and Stability/Instability | 11 | 14 |
12 | ILD and Rolling Loads | 6 | 11 |
13 | Arches | – | 6 |
14 | Methods of Indeterminate Analysis | 13 | 30 |
15 | Trusses | 8 | 6 |
16 | Matrix Methods of Analysis | 5 | 3 |
An analysis of last 5 years of GATE papers reflect that SOM and Structures combined carry 10-15 marks, which is huge! And considering their importance in interviews also, this subject needs thorough preparation.
Time required for preparation
20-25 days (if you have 8-10 month of preparation) with 3-4 hours daily
10-12 days (if you have 4-5 months of preparation) with 6-8 hours daily
Both SOM & Structural Analysis will have mostly numerical questions, with equal weightage in 1-mark and 2 mark questions. There are some formulas which you should remember, which I will specifically mention; and it is better to make a formula sheet for future revision. The textbook(s) to be referred are mentioned in a separate comprehensive blog which you should refer.
Let’s start our topic-wise discussion (most important concepts are bold & italics):
1. PROPERTIES OF MATERIAL, SIMPLE STRESS-STRAIN & ELASTIC CONSTANTS (3 DAYS)
This chapter forms the basis of Civil Engineering. It is very important from point of view of interviews also. This is the only chapter from which theoretical questions are more commonly asked.
Stress-strain graph for different kind of materials; some basic definitions like ductility, brittleness, hardness, etc, can come as match the following type questions; relations b/w Elastic constants (E, G, K, µ) should be remembered.
Axial displacements in bars, tapered bars, thermal stresses, compound bar subjected to thermal stresses, nut-bolt assembly. Practice numericals on these topics.
2. SFD and BMD (3 DAYS)
The most important topic in SOM as this will form the basis of Structural Analysis also. Many questions are asked in interviews. Thorough understanding of this topic is highly recommended..!
Relation b/w loading, SFD and BMD shapes; SFD and BMD of simply-supported beams and cantilevers for various loading (point load, UDL, UVL, concentrated moment) and introduction of special conditions such as hinges in beams. Practice as much numericals possible as there is a lot of variety.
3. PRINCIPAL STRESS-STRAIN & THEORIES OF FAILURE (2 DAYS)
Analytical formula for finding Principal Stresses and directions, Visualization of Analytical solution as a Mohr Circle of Stresses;
Relation b/w Principal Strain & Stresses (using µ), analytical formula for finding Principal Strains, Mohr Circle of Strains, Strain rosette (90⁰, delta and star formation).
Theories of failure: Max principal stress, Max principal strain, Max shear stress (most common)¸ Max strain energy and Max distortion energy. Match the following question(s) relating these theories to their applicability and FOS is very probable.
4. BENDING STRESSES IN BEAMS (1 DAY)
Bending Stresses vary linearly in case of pure bending, being zero at Neutral Axis (NA):
Analysis of flitched section (timber & steel), equivalent section of flitched section. Practice numericals of flitched sections (both top-bottom & side flitching).
5. SHEAR STRESSES IN BEAMS (1 DAY)
Shear Stresses vary parabolically in beams, being zero at top & bottom. Also, shear stress at a section is inversely proportional to width (B) at that section. You may not remember formula for each cross-section, but you should remember relation b/w τ(max), τ(NA) and τ(average), which will be used in numericals.
Shear Stress distribution in H, I and T-sections (as a consequence of change in width); diamond section.
6. SLOPE & DEFLECTION OF BEAMS (3 DAYS)
This is a topic from which a question is surely asked. Understanding of this topic will be required in Structural Analysis also. This topic is also very important for interviews.
Firstly & most importantly, standard results of slope and deflection of simply-supported beam & cantilever for all kinds of loading should be remembered (write in formula sheet).
Then, understanding of Moment-Area (Mohr’s) method should be clear, this is helpful in many numericals. Practice numerical which utilize Mohr’s method (you may not realize that a question requires use of this method until you get the hang of it). McCaulay’s method can be read once (but it is not much helpful in objective questions).
Lastly, conjugate beam method (qualitatively from the point of view of end-conditions) should be read.
Practice many numericals for Slope & Deflection as there is a lot of variety.
7. THICK & THIN CYLINDERS AND SPHERES (1/2 DAY)
Formula based topic. A theoretical match the following type question based on nature of stress (compressive or tensile) inside cylinder/sphere can be asked.
You should write down formulas of Hoop stress, Longitudinal stress, Circumferential strain, Longitudinal strain and Volumetric strain for thin cylinder and thin spheres in your formula sheet for revision later.
For thick cylinder, Lame’s theory is used. Remember formula for Hoop and Longitudinal Stress (values of constants A & B) and qualitative variation of these stresses along the thickness of cylinder.
8. TORSION IN SHAFTS & SPRINGS (1 DAY)
Just like pure bending, pure torsion has linear shear stress behavior, being zero at Neutral Axis (NA):
Torsion along constant/variable cross-section of circular bar, Power transmitted by torque, and combined action of Moment and Torque (this utilizes analytical principal stress result) are important topics.
Combination of springs in series and parallel, closed coil helical spring, open coil helical spring and leaf spring are small topics which can be directly done through formulas also. A question on cutting one spring into multiple springs is more common.
9. THEORY OF COLUMNS (1 DAY)
This is a very easy and scoring topic from which one question can be almost surely expected from: Euler’s buckling load, end conditions and effective length of column (practice numericals of all types of end conditions). Euler’s curve for crushing and buckling for long columns should also be read.
Another important concept in this topic is combined axial and bending forces, which has just one formula and one direct application to find core (kern) of a section.
10. CENTROID, MOMENT OF INERTIA & SHEAR CENTRE (1/2 DAY)
Very rarely, a question may be asked from this topic. Shear centre of some sections can be directly learned. Centroid of parabola (both convex and concave parts) should be known. Practice one or two numericals for parallel axes and perpendicular axes theorem which will be enough.
STRUCTURAL ANALYSIS
11. DETERMINACY/INDETERMINACY AND STABILITY/UNSTABILITY (1 DAY)
Trust me…one sure question, every year! And trust me again…very easy to make mistakes!
Static (D_{s}) and Kinematic (D_{k}) Indeterminacy, Truss and Frame, 2D and 3D: these are all possible combinations. As much important it is to know the formula for each case, it is equally important to know how to apply them, what are axially rigid members, and how do hinges play a role in increasing D_{k} or decreasing D_{s}. Understand properly both internal and external stability.
Write down formulas in the formula sheet and practice a lot of numericals; you would not want to miss out on those sure shot marks!
12. ILD AND ROLLING LOADS (1 DAY)
Muller Breslau’s principle for qualitative idea of ILD is important. Then, the most important concept is movement of series of wheel loads on a beam: Centre of beam is midway b/w CG of wheel loads and load under consideration. 90% of the times a question will be asked from this concept.
Another concept to learn is introduction of hinges in continuous beam and then finding out ILD of various supports. Practice 2-3 numericals for each concept.
13. ARCHES (1/2 DAY)
3-hinged arch questions are more common for which you should remember the equation of parabolic arch and proceed similar to a beam (remember that BM at hinge is zero!).
A theoretical question from 2 hinge arch (mostly from temperature change) or linear arch may be asked.
14. METHODS OF INDETERMINATE ANALYSIS (2 DAYS)
All these are displacement methods of analysis and include slope-deflection, moment distribution, Castigliano’s method and column analogy methods. Since these methods themselves are lengthy as a whole, sub-topics which are very important are:
Fixed end moments (learn & note in formula sheet), near and far end moments, moment due to support sink, sway of frame (qualitative), Distribution factors (and ratio). These topics are directly utilized further in Sl No. 16 below.
Practicing 1-2 full conventional question from each topic will clear all these concepts in single go! Or you can practice 5-10 small questions from each topic to cover these aspects.
15. TRUSSES (1 DAY)
Members carrying 0-force is a most probable question from this topic. Apart from this, application of method of sections, strain energy method and ILD of truss can be asked. Practice 1-2 numericals each.
16. MATRIX METHODS OF ANALYSIS (2 DAYS)
This contains 2 parts – Flexibility matrix and Stiffness matrix. This is the 2^{nd} most important & asked topic in Structural Analysis after indeterminacy nowadays, and is very easy & scoring.
Practice 3 questions each of stiffness matrix and flexibility matrix (this will require direct utilization of concepts of sub-topics mentioned in Sl No. 14 above).