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ADVANCE STRUCTURAL ANALYSIS – KCE-061
Section-wise Important Questions & Ready Answers
SECTION A
(Attempt all – short answers)
(a) Application of Fixed Beam
A fixed beam is commonly used in building floors, bridges, and frames where end rotations are restrained. It provides higher stiffness and smaller deflections compared to simply supported beams, making it suitable for heavy loading conditions.
(b) Steps in Slope Deflection Method
The slope deflection method involves fixing all joints, calculating fixed end moments, writing slope deflection equations considering joint rotations and settlements, applying equilibrium conditions, and finally computing member end moments and reactions.
(c) Use of Müller–Breslau Principle
The Müller–Breslau principle is used to determine influence lines for reactions, shear force, and bending moment in statically determinate and indeterminate structures.
(d) Application of Two-Hinged Arch
Two-hinged arches are used in bridges and roofs where thermal expansion and settlement effects must be accommodated while still providing structural stiffness and economy.
(e) Application of Influence Line
Influence lines are used to determine maximum shear force, bending moment, or reaction at a specific point due to moving loads, especially in bridges and cranes.
(f) Usefulness of Suspension Bridges
Suspension bridges are useful for very long spans because they efficiently carry loads through tension in cables, reducing material requirement and allowing large clearances.
(g) Matrix Force Method of Analysis
The matrix force method is a flexibility-based approach where unknown forces are treated as primary variables and compatibility equations are solved using matrix algebra.
(h) Displacement Method Also Known As
The displacement method is also known as the stiffness method or matrix displacement method.
(i) Main Aim of Plastic Analysis
The main aim of plastic analysis is to determine the ultimate load-carrying capacity of structures beyond elastic limits and achieve economical design.
(j) Kinematic Method of Plastic Analysis
The kinematic method is an upper bound method where collapse mechanisms are assumed and external work is equated to internal plastic work to find collapse load.
SECTION B
(Attempt any three – descriptive answers)
2(a) Moment Distribution Method – Procedure
The moment distribution method is used for indeterminate beams and frames. The structure is first assumed fully fixed. Fixed end moments are calculated, distribution factors are determined based on stiffness, and unbalanced moments at joints are distributed iteratively until equilibrium is achieved. Final bending moments are used to draw BMD and SFD.
2(b) Horizontal Thrust in Two-Hinged Parabolic Arch (UDL)
For a two-hinged parabolic arch of span l and rise h carrying UDL w over the entire span, the horizontal thrust at each support is:
H=wl28hH = \frac{w l^2}{8 h}H=8hwl2
This thrust balances the bending effect and reduces bending moments in the arch.
2(c) Analysis of Two-Hinged Stiffening Girder
The analysis involves calculating dead and live load effects, determining horizontal thrust from the cable, finding bending moments in the stiffening girder using influence lines, and ensuring compatibility between cable and girder deformations.
2(d) Stiffness Method – Step by Step Procedure
The stiffness method includes defining degrees of freedom, calculating member stiffness matrices, assembling global stiffness matrix, applying boundary conditions, solving for joint displacements, and finally computing member forces and reactions.
2(e) Application of Plastic Analysis in Design
Plastic analysis allows redistribution of moments after yielding. For example, in continuous beams, plastic hinges form at critical sections, enabling full utilization of material strength and resulting in economical design compared to elastic analysis.
SECTION C
(Attempt any one part)
3(a) Continuous Beam by Moment Distribution (with Settlement)
When a support sinks, additional moments due to settlement are calculated using slope deflection equations. Fixed end moments, carry-over moments, and settlement effects are combined to obtain final bending moments and draw BMD.
3(b) Continuous Beam by Slope Deflection Method
Slope deflection equations are written for each member considering rotations and fixed end moments. Joint equilibrium equations are solved to obtain rotations, after which end moments and bending moment diagram are drawn.