Structural Analysis-I — Summer 2024

State assumptions and limitations of Euler’s formula.

Write Euler’s formula and explain the effective length of the column for different end conditions with a neat sketch.

Asteel bar 100 cm long and rectangular in section 40 mm x 80 mm is subjected to an axial load of 1 kN. Find the maximum stress if (i) The load is applied gradually (ii) The load is applied suddenly, and (iii) The load is applied after falling through a height of 8 cm. What are the strain energies in each of the above cases? Take E = 200 GPa.

State and explain the principle of superposition.

Explain various types of framed structures with distinguishing features of each.

Determine the slope and deflection at the free end of a cantilever beam AB of span 2 m subjected to a load of 30 KN at free end B. Take I =6x107 mm4 and E= 2x105 N/mm2 by using moment area method. xx

Ahollow cast iron section having external diameter 250 mm and thickness 25 mm is used as 4.5 m long column with both ends fixed. Find the safe load by (a) Euler’s formula & (b) by Rankine’s formula. Take factor of safety=3.5 ,Compressive stress= 500 N/mm2, α= 1/1600,E= 0.14x105 N/mm2

Define the followings: (a) Radius of Gyration, (b) Slenderness Ratio and

Critical Load.

Explain Maxwell’s theorem of reciprocal deflections.

Acylindrical shell 3 m long & 1m diameter is subjected to an internal pressure of 1 N/mm2. If the thickness of the shell is 12 mm. Find the circumferential stress, longitudinal stress & change in the dimensions of the shell. Take E= 2 x105 N/mm2 , Poisson’s ratio (1/m)=0.27

Derive the relation between slope, deflection and radius of curvature of the beam.

Explain any two stability conditions for retaining wall.

Apropped cantilever beam AB of span 5 m carries a point load of 30 KN at 2 m from the left support A. Analyse the beam using consistent deformation method and draw S.F.D. and B.M.D.1

Define: (i) Resilience (ii) Proof Resilience and (iii) Modulus of resilience.

State advantages and disadvantages of fixed beam over simply supported beam.

Amasonry dam 6 m high, 3 m wide at base and 1.2 m wide at top, retains water on vertical face for full height. Considering density of masonry as 17 KN/m3 and density of water as 10 KN/m3, find out maximum and minimum pressure intensities at the base.

Derive the equation for Strain Energy stored in a bar due to Sudden Loading.

State Moment Area theorems Iand II.

Athree-hinged parabolic arch having span of 20 m and central rise 3m carries a point load of 10 KN at 7.5 m from the left hand hinge. Calculate the reactions developed at Supports. Also find the (i) Bending Moment, (ii) Normal Thrust and (iii) Radial Shear at point 7.5 m from right end hinge.

Differentiate between real beam and conjugate beam. Justify the support condition in the conjugate beam.

Discuss various types of Arches.

Afixed beam of 5 m span carries a central point load of 40 KN. Find out the fixed end moments and draw SFD & BMD of the beam.

Explain direct stress and bending stress.

Define and explain : Kernel of rectangular section.

Abar 54 mm in diameter is 4 m long. An axial load of 180 KN is suddenly applied to it. Find (i) maximum instantaneous stress (ii) maximum elongation & (iii) Strain energy. Take E= 2 x 105 N/mm2