JNTU
JNTU B.Tech III ADVANCED STRUCTURAL ANALYSIS Previous Question Paper (January/February - 2021 - R16)
Answer any five questions. All questions carry equal marks.
Main
A two-hinged parabolic arch has a span of 25 m and rise 5 m the section of the arch varies such that its moment of inertia is proportional to the secant of the slope of the arch axis. Determine the maximum bending moment at a section 5 m from the left support when a point load of 65 kN acts at a distance of 6 m from right support.
Answer
For a two-hinged parabolic arch where the moment of inertia varies as I = I0 sec θ, the horizontal thrust H is given by the formula:
Given: Span L = 25 m, Rise r = 5 m, Point load W = 65 kN at b = 6 m from the right support. The distance from the left support is a = L - b = 25 - 6 = 19 m.
Substituting the values into the horizontal thrust equation:
To find the bending moment at x = 5 m from the left support, first calculate the vertical reaction at the left support VA using equilibrium:
The equation for the rise of the parabolic arch at distance x is:
The bending moment Mx at x = 5 m is calculated as:
The maximum bending moment at the section 5 m from the left support is 331.032 kNm (hogging).
Determine the vertical displacement of joint A in figure 1. Take A = 1000 mm2 and E = 200 kN/mm2.
Answer
To determine the vertical displacement of joint A using the unit load method (or virtual work method), we apply a virtual unit load at joint A in the vertical direction. The vertical displacement Δ is given by the formula:
Where:
- P is the internal force in each member due to the actual external loads.
- u is the internal force in each member due to a virtual unit load applied at joint A in the vertical direction.
- L is the length of each member.
- A is the cross-sectional area (1000 mm2).
- E is the Young's modulus (200 kN/mm2).
Step 1: Analysis of actual forces (P). Calculate the support reactions and determine the axial forces in all members of the truss under the given external loading using the method of joints or method of sections.
Step 2: Analysis of virtual forces (u). Remove all actual external loads and apply a vertical unit load (1 kN) at joint A. Calculate the resulting internal axial forces in all members.
Step 3: Tabulation and Summation. Create a table with columns for Member, L, P, u, and (u ⋅ P ⋅ L). Sum the values in the final column to find Σ(u ⋅ P ⋅ L).
Step 4: Final Calculation. Substitute the values into the displacement formula:
Ensure that units are consistent (kN and mm). The resulting displacement Δ will be in millimeters. If the sum is positive, the displacement is in the direction of the assumed unit load (downward); if negative, it is upward.
Use slope-deflection method to determine the end moment in a rectangular bent shown in figure 2. Draw the BMD.
Answer
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Analyse the frame of figure 3 by moment distribution method. Draw BMD.
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Using Kani’s method, analyse the three-span continuous beam load as in figure 4, if the moment of inertia of spans AB, BC, CD is I, 2I and 1.5I respectively. Sketch the BM.
Answer
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Determine the member end moments for the frame shown in figure 5 by Kani’s method.
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Analyse the continuous beam shown in figure 6 by stiffness method.
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Construct the influence line for shear at point D which is the mid-span of member AB shown in figure 7. Compute the value of the maximum shear at D if the beam carries a UDL of 10 kN/m and the UDL can occupy a single span fully. Assume EI is constant.
Answer
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