B.TECH - Semester 4 structural analysis i Question Paper 2019 (jun)
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- Draw the ILD for shear force and bending moment of a cantilever carrying a point load at a distance 'a' from the free end. $$ (8 \times 5=40 \text { Marks }) $$ Answer one full questions from each Module. Each question carries 20 marks.
- Two point loads of 100 kN and 200 kN spaced 3 m apart cross a girder of span 15 m from left to right with the 100 kN load loading. Draw influence line for shear force and bending moment and find the value of maximum shear force and bending moment at a section 6 m from the left hand support. Also, fi...
- A propped cantilever beam is subjected to uniformly distributed load over the entire span. If an internal hinge is provided at the mid-span location, draw the conjugate beam (with appropriate supports and loading shapes) that can be used for calculating displacement responses of the real beam?
- What are the limitations of Euler's formula?
- Two wheel loads 80 kN and 200 kN spaced 2 m apart move on a girder of span 16 m , Find the maximum positive and negative shear force at a section 4 m from the left end. Any wheel load can lead the other. Answer one full question from each module
- Find the rotation at supports of a simple beam when it is subjected to a central load $W$ and the moment of inertia of portion $L / 4$ of the beam on either side of mid-span is $4 I$ and the remaining $\mathrm{L} / 4$ portion near either support is $2 I$.
- Determine the vertical displacement of the joint B and the relative displacement of the joints $A$ and $C$ in the pin-jointed plane frame as shown in figure below. The areas of cross section of the members in $\mathrm{mm}^{2}$ are indicated alongside the members. Take $\mathrm{E}=200 \mathrm{GPa}$. ...
- Using energy method, find deflection at centre of span $A B$ of a over-hanging beam $A B C$ shown in figure below. Take $E=200 \mathrm{GPa}$ and $\mathrm{I}=800 \times 10^{6} \mathrm{~mm}^{4}$.
- A hollow cylindrical cast iron column is 4 m long, both ends being fixed. Design the column to carry an axial load of 250 kN . Use Rankine's formula and adopt a factor of safety of 5 . The internal diameter may be taken as 0.80 times the external diameter. Take $\mathrm{F}_{\mathrm{c}}=550 \mathrm{M...
- Find the bending moment at a section 4 m from the left end of a three hinged parabolic arch due to udl of $10 \mathrm{kN} / \mathrm{m}$ over entire span 30 m .
- What are the various stresses set up in the column?
- A cantilever 2 m long is loaded with a point load of 1.4 kN at free end and distributed loaded load of 3.4 kN per meter run over 1.2 m from the fixed end. If the section is rectangular $80 \mathrm{~mm} \times 160 \mathrm{~mm}$. calculate the slope and deflection at the free end. Take $E=1 \times 10^...
- Find an expression for the strain energy due to bending foe a beam of length L simply supported at the ends and carrying a uniformly distributed load w per unit run over whole of its span. The beam is of constant cross section throughout its length having flexural rigidity as EI. Module - II
- The cross sectional area of each member of the truss shown in the figure is $400 \mathrm{~mm}^{2}$ and $\mathrm{E}=200 \mathrm{GPa}$. Using the principle of virtual work determine the vertical displacement of joint C is a 4 kN force is applied to the truss at C .
- A three hinged circular arch of span 16 m and rise 4 m is subjected to two point loads of 100 kN and 80 kN at the left and right quarter span points respectively. Find the reactions at supports. Find also the bending moments, radial shear and normal thrust at 6 m from the left support.
- A short length of tube 4 cm internal diameter and 5 cm external diameter failed in compression at a load of 240 kN . When a 2 m length of the same tube was tested as a strut with fixed ends, the load was 158 kN . Assuming that 'a' in Rankine's formula is given by the first test, find the value of th...
- Define Castigliano's theorems.
- A simply supported beam of span 5 m is subjected to a concentrated load of 50 kN at 2 m from the left support. If the Young's modulus is $200 \mathrm{kN} / \mathrm{mm}^{2}$ and moment of inertia is $5 \times 10^{-5} \mathrm{~m}^{4}$, determine the slope and deflection at mid-span using conjugate-bea...
- A three hinged parabolic arch $A C B$ is hinged at the supports $A$ and $B$ which are below the crown hinge C by 3 m and 6.75 m respectively. The span of the arch is 22.5 m . The arch carries a udl of $30 \mathrm{kN} / \mathrm{m}$ from A to C. Find the reactions at the supports and the maximum posit...
- Two concentrated loads of 50 kN and 75 kN separated by 4 m rolls across a beam of 12 m span from left to right with 50 kN load leading the train. Draw the maximum SFD and BMD. Also, locate the position and calculate the magnitude of the absolute maximum bending moment.
- A girder simply supported has a span of 24 m . A udl of intensity $20 \mathrm{kN} / \mathrm{m}$ and 6 m long crosses the girder. Using influence line diagrams find the maximum shear force and bending moment at a section 9 m from the left support. ( $\mathbf{4} \boldsymbol{\times} \mathbf{2 0} \bolds...
- A prismatic column is fixed at the ends. Derive the expression for Euler buckling load.
- State the theories of the conjugate beam method.
- How do you differentiate the static indeterminacy from the determinacy of the structures?
- Derive Maxwell's reciprocal theorem.
- Write the principle and procedure for tension coefficient method.
- Show the failure of short and long column with neat sketches.
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