Analysis and Design of Structures - short answer type questions from AMIE exams (Summer 2019)

Answer the following (10 x 2)

Define the Distribution factor used in the Moment Distribution Method.
Consider a joint in a structure where two or more members meet. If an external moment M is applied to such a joint, the joint undergoes a rotation θ. Since all the members meeting at this joint undergo the same rotation θ. the applied moment M is distributed to each of the ends of the members according to their relative stiffness values. The factor by which the applied moment is multiplied to obtain the end moment of any member is known as the distribution factor (D.F.).

State Castigliano’s Second Theorem.
Castigliano’s Second Theorem: If a linearly elastic structure is subjected to a set of loads, the displacement of any load in its direction is equal to the partial derivative of the total strain energy with respect to that load.

\frac{{\partial U}}{{\partial {P_i}}} = {\Delta _i}

Pi and Dcan also be the moment and the angular rotation respectively.

State relationship between Flexibility and Stiffness matrix
The element stiffness matrix 'k' is the inverse of the element flexibility matrix 'f' and is given by f=1/k or k =1/f.

When the Moment Area method is preferred to calculate Deflection. Explain?
The moment-area method of determining deflections provides a convenient means of determining slopes and defections in beams and frames. This is a semi-graphical method and can be conveniently used for members of the varying moments of inertia and discontinuous loadings.

Differentiate between lacing and battens.

Lacing
The lacing is also termed as ‘latticing’ and it is most commonly used. The rolled steel flats, angles and channels are used for lacing. The rolled steel sections or tubes of equivalent length may also be used instead of flats. The lacing is of two types: (i) Single lacing (ii) Double lacing.

Battens

The batten plates are also called the plates, and these are also used in the lateral systems. The angle sections, channels and I-sections are also used as battens. The components of the built-up column sharing the load are connected together by batten plates.

Battened plates

Write a short note on Plastic Analysis?
Elastic behaviour of structures is useful to study the performance of the structure, especially with regard to serviceability under working load. However, in steel structures, if the load is increased, some of the sections in the structure may develop yield stress. Any further increase in load causes the structure to
undergo elastoplastic deformations and some of the sections may develop a fully plastic condition at which a sufficient number of plastic hinges are formed transforming the structure into a mechanism. The mechanism would collapse without noticeable additional loading. 
A study of the mechanism of failure and knowledge of the load causing the mechanism is necessary to determine the load factor. A structure is designed so that its collapse load is equal to or higher than the working load multiplied by the load factor specified. Design of structures based on the plastic approach is being increasingly used and adopted in various codes of practice, particularly for steel structures. 

Compare riveted, welded and bolted connections.
  • Welded joints arc economical. This is because splice plates and rivet materials are eliminated. Also, the gusset plates required are of smaller size because of the reduced connection length. Labour cost is also less as only one person is required to do the welding whereas at least four persons are required for riveting.
  • Welded structures are more rigid (due to the continuity of the section at the joint) as compared to riveted joints. In riveted joints, cover plates, connecting angles, etc. deflect along with the member during load transfer and make the joint more flexible.
  • Due to the fact that the strength of a welded joint is the same as that of the parent metals, even the smallest piece of the metal which otherwise is a scrap can be used, bringing overall economy.
  • With welding, it has become possible to connect tubular sections, which arc structurally very economical.
  • Duc to the fusion of two metal pieces jointed, a continuous structure is obtained, which gives a better architectural appearance than riveted joints.
  • Alterations can be done with fewer expenses in the case of welding as compared to riveting.
  • The process of welding is quicker in comparison to riveting.
  • The process of welding is silent, whereas in the case of riveting a lot of noise is produced.
  • In welding, less safety precautions are required for the public in the vicinity, whereas a hot rivet may toss and injure the persons working.
  • As splice plates, rivets, etc. are not used, the details and drawings of welded structures are easier and less time-consuming.
  • The efficiency of a welded joint is more than that of a riveted joint. In fact, a properly welded joint may have 100% efficiency.
  • Members to be jointed may distort due to the heat during the welding process, whereas there is no such possibility in riveted joints.
  • The possibility of a brittle fracture is more in the case of welded joints as compared to riveted joints.
  • The inspection of welded joints is difficult and expensive, whereas riveted joints can be inspected simply by tapping the joint with a hammer.
  • A more skilled person is required to make a welded joint as compared to the riveted joint.
Explain the following terms - pitch, gauge, end distance and edge distance

Pitch of Rivet (p)
The pitch of rivets is the distance between two consecutive rivets measured parallel to the direction of the force in the structural member, lying on the same rivet line. It is the centre to centre distance between the individual fasteners. 

Gauge Distance of Rivets (g)
The gauge distance is the transverse distance between two consecutive rivets of adjacent chains (parallel adjacent lines of fasteners) and is measured at right angles to the direction of the force in the structural member.


Edge Distance
A minimum edge distance of approximately 15 times the gross diameter of the rivet measured from the centre of the rivet hole is provided in the riveted joint.


Write steps for the design of welded plate girder.
Various steps are
  • Design of web
  • Design of flanges
  • Design of connection of flange plate and web
  • Design of bearing stiffener
  • Design of Intermediate stiffeners
Differentiate between flexibility and stiffness matrix method of analysis?

Flexibility matrix method
  • The redundant forces are treated as basic unknowns.
  • The number of equations involved is equal to the degree of static indeterminacy of the structure.
  • The method is the generalization of the consistent deformation method. 
  • Different procedures are used for determinate and indeterminate structures
Stiffness matrix method
  • The joint displacements are treated as basic unknowns
  • The number of displacements involved is equal to the no of degrees of freedom of the structure
  • The method is the generalization of the slope deflection method.
  • The same procedure is used for both determinate and indeterminate structures.
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