### Analysis and Design of Structures - objective questions from AMIE exams (Winter 2019)

*Fill in the blanks with appropriate words (5 x 2)*

1. The simply supported beam of length L loaded with a uniformly distributed load of W per unit length. The maximum deflection will be ⸺

Answer: 5WL⁴/384EI

2. Redundant frames may be analysed by ⸺

Answer: Castigliano's second theorem.

- Castigliano’s second theorem: The first partial derivative of the total internal energy in a structure with respect to the force applied at any point is equal to the deflection at the point of application of that force in the direction of its line of action.
- The second theorem of Castigliano is applicable to linearly elastic structures with constant temperature and unyielding supports.

3. A three-hinged semicircular arch of radius "r" is subjected to a uniformly distributed load of‘ W per unit length on the whole span. The horizontal thrust will be given by ⸺

Answer: Wr/2

∑M

_{A}= 0V

_{B}X 2r - W X r X 2r = 0V

_{B}= W x r∑V = O

V

_{A}= V_{B}= W x rM

_{C}= 0V

_{B}x r — W x r x r/2 = H_{B}x rH

_{B}= Wr/24. The size of a rivet is expressed by ⸺

Answer: diameter of the shank.

5. The web of a plate girder may fail due to ⸺

Answer: diagonal compression

Near the supports due to high shear in the web severe diagonal tensile and compressive stresses may be developed. The thin web, though can resist the diagonal tensile stresses, may not be strong enough to resist the diagonal compressive stresses and as such is liable to buckle.

*Answer the following in brief ( 5 x 2)*

**Define factor of safety, slip factor, clamping force for bolted joint.**

**Factor of safety.**The factor of safety is the numerical value by which the load which would cause slip in a joint is divided to give the permissible working load on the joint.**Slip factor.**The slip factor is defined as the ratio of the load per effective interface, required to produce slip in a pure shear joint to the total shank tension induced in the bolts.**Clamping force.**Clamp force is what holds a bolted joint together.

**What do you understand by buckling of the column?**

Buckling of Columns is a form of deformation as a result of axial-compression forces. This leads to a bending of the column, due to the instability of the column. This mode of failure is quick and hence dangerous. Length, strength and other factors determine how or if a column will buckle.

P = nĎ€²EI/L²

The ‘L’ in this equation symbolizes length and ‘P’ symbolizes the allowable load before buckle. As the length increases, the allowable load decreases. With shorter columns compared to its thickness, one can infer from the same equation above that the allowable stress on a column before buckling increases as length decreases.

**Name the various loads acting on Gantry Girder.**

Type of Load on Gantry Gutter

- Vertical Loads on Gantry Gutter.
- Lateral Loads on Gantry Gutter.
- Longitudinal Loads on Gantry Gutter.
- Impact Loads on Gantry Gutter.

**Define the terms ‘Bay’, ‘Rise’, ‘Span’, ‘Pitch, ‘Slope’ in truss design.**

**Span**The span of a roof truss is defined as the distance between the centre to the centre of supports. The span of a roof truss is decided by the dimensions of the area to be kept free of columns.**Rise**The rise of a roof truss is defined as the distance from the highest point to the line joining supports.**Pitch**The pitch of a symmetrical truss is defined as the ratio of the rise to the full span.**Slope**The slope of a symmetrical truss is defined as the ratio of the rise to half the span.**Bay**The bay is defined as the distance between the adjacent trusses

**List out the various likely modes of failure due to combined bending and axial load in a beam-column.**

A beam-column connection can be subjected to either axial load or bending (both uniaxial and biaxial) or torsion or any combination of these. Hence, there exist several failure mechanisms of beam-column connection. Generally, the following mechanism is likely to be the mode of failure:

- Axial compression and bending about one axis: Failure by instability in the plane of bending without twisting.
- Axial compression and bending about the strong axis: Failure by lateral-torsional buckling.
- Axial compression and biaxial bending (torsionally stiff sections): Failure by instability in one of the principal directions.
- Axial compression and biaxial bending (thin-walled sections): Failure by combined twisting and bending on these torsionally weak sections.
- Axial compression, biaxial bending, and torsion: Failure by combined twisting and bending when the plane of bending does not contain the shear centre.

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