JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year STRUCTURAL ANALYSIS - II Previous Question Paper (February - 2022 - R18)
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Main
An RCC two-hinged parabolic arch has 40 m span and central rise of 6 m, is subjected to a concentrated load of 90 kN at centre. Determine the horizontal thrust, if the arch is subjected to rise in temperature of 30℃. The second moment of the area of the arch rib varies as the secant of the slope of the rib axis. Assume the cross-section of the arch is 900 mm × 400 mm and concrete of grade M35.
Answer
For a two-hinged parabolic arch where the moment of inertia varies as the secant of the slope (I = I0 sec θ), the horizontal thrust due to a temperature rise (Δt) is given by the formula:
Given data:
- Span (L) = 40 m
- Rise (h) = 6 m
- Temperature rise (Δt) = 30°C
- Cross-section = 900 mm × 400 mm = 0.36 m2
- Coefficient of thermal expansion (α) = 12 × 10-6 /°C (standard for concrete)
- Modulus of elasticity (E) for M35 concrete = 5000 √fck = 5000 √35 ≈ 29580 N/mm2 = 29.58 × 106 kN/m2
The horizontal thrust due to temperature change is independent of the moment of inertia I0 in this specific variation model, as the effect of rib shortening is often neglected unless specified. However, the standard expression for horizontal thrust due to temperature in a two-hinged parabolic arch is:
Substituting the values:
The horizontal thrust due to the concentrated load of 90 kN at the center is calculated as:
The total horizontal thrust is the sum of the thrust due to the load and the thrust due to the temperature rise:
Using moment distribution method, analyse the frame shown in figure 1 and draw the bending moment diagram and Elastic curve.
Answer
To analyze the frame using the Moment Distribution Method (MDM), we first determine the stiffness factors and distribution factors for each joint. For a frame with members of uniform cross-section, the stiffness is 4EI/L for fixed ends and 3EI/L for pinned ends. Distribution factors (DF) are calculated as the ratio of the member stiffness to the total stiffness of all members meeting at that joint.
The steps for the analysis are as follows:
- Calculate the fixed end moments (FEM) for all loaded members based on the applied external loads.
- Determine the distribution factors at each rigid joint.
- Perform the distribution process by iteratively balancing the joints. At each joint, the unbalanced moment is distributed to the connected members in proportion to their distribution factors.
- Apply carry-over moments to the far ends of the members (half of the distributed moment is carried over to the fixed end).
- Repeat the distribution and carry-over process until the unbalanced moments at all joints are negligible.
- Sum all moments at each joint to obtain the final end moments.
Once the final end moments are obtained, the bending moment diagram is constructed by plotting the end moments and superimposing the free bending moment diagrams due to external loads. The elastic curve is sketched based on the signs of the final moments: positive moments cause sagging (tension at the bottom), and negative moments cause hogging (tension at the top), with the curvature consistent with the deflected shape of the frame members under the applied loads.
Using Kani's method, analyze the frame shown in figure 2 and draw the bending moment diagram. Elastic curve.
Answer
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A suspension bridge of 150 m span has two three-hinged stiffening girders supported by two cables with a central dip of 15 m. If four concentrated loads of 125 kN each are placed along the centre line of the roadway at 15 m, 30 m, 45 m and 60 m from the right end. Find the shear force and bending moment at a section located at 50 m from the right end, in each girder. Also find the maximum tension in the cable.
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Using Portal method, analyze the plane frame shown in figure 3. And draw the bending moment diagram.
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In a multi-storeyed building the frames, as shown in figure 4, are spaced at 3.6 m c/c. The dead and live loads carried by the slab are 1 kN/m2 and 3 kN/m2 respectively. Using substitute frame method, analyse an intermediate span of the first floor for maximum negative bending moment.
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Using the stiffness method, analyze the frame supported and loaded as shown in figure 5.
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Draw the influence line diagram for the reaction at the left support of a continuous beam shown in figure 6.
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