This blog is the 5th article in a series of GATE preparation tips blog articles for Civil Engineering Students. The blog author, Rohit Sachdeva has secured AIR 93 in GATE 2017 and is currently studying at IISc Bangalore. You can read the rest of the articles under the CE section for GATE blogs at http://gate.vidyalankar.org/category/civil-engineering/.
In this blog, I will discuss how to prepare a subject that is considered one of the most difficult in Civil Engineering: SOM or Solid Mechanics. Not only does this subject carry significant weightage in GATE, but is also a favorite among many interviewers in both PSUs and IITs. Anyone who considers pursuing their career as a Structural Engineer will have to deal with these concepts throughout their life. SOM also forms the backbone of Structural Engineering (BLOG 6), which is 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:
||No. of Questions
||Properties of Material, Simple Stress-Strain & Elastic Constants
||SFD and BMD
||Principal Stress-Strain & Theories of Failure
||Bending Stresses in Beams
||Shear Stresses in Beams
||Slope & Deflection of Beams
||Thick & Thin Cylinders and Spheres
||Torsion in Shafts & Springs
||Theory of Columns
||Centroid, Moment of Inertia & Shear Centre
An analysis of last 5 years of GATE papers reflects that SOM and Structural Analysis combined carry 10-12 marks, which is huge! And considering their importance in interviews too, this subject needs thorough preparation.
Time required for preparation
12-15 days (if you have 8-10 month of preparation) with 3-4 hours daily
7 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 BLOG-3 which you can utilize.
A topic-wise discussion is as follows, with most important concepts in bold & italics:
1. PROPERTIES OF MATERIAL, SIMPLE STRESS-STRAIN & ELASTIC CONSTANTS (3 DAYS)
This chapter forms the basis of Structural Engineering. It is very important from point of view of interviews as well. This is the only chapter from which theoretical questions are more commonly asked.
Stress-strain graph for different type of materials; basic definitions like ductility, brittleness, hardness, etc, can come as match the following type questions; relations between Elastic constants (E, G, K, µ) should be remembered and included in your formula book.
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 are hot topics. 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 their directions, Visualization of Analytical solution as a Mohr Circle of Stresses; Relation between Principal Strain & Stresses (using Poisson’s ratio), analytical formula for finding Principal Strains, Mohr Circle of Strains, Strain rosette (90⁰, delta and star formation).
(I suggest to include the Mohr circles for special conditions of stresses in your formula book)
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):f/y=M/I=E/R
Analysis of flitched section (timber & steel), equivalent section of flitched section, horizontally and vertically joined steel sections. 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 be able 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. These can be included in your formula book for easy reference.
6. SLOPE & DEFLECTION OF BEAMS (3 DAYS)
This is a topic from which a question is surely asked every year. 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 very 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 DAYS)
This is a 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 cylinders, Lame’s theory is used. Remember the 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):f/r=T/J=Gθ/L
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 DAYS)
Very rarely, a question can be asked from this topic. Shear centre of common 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.