DESIGN OF STRUCTURE – I (RCE-502)
B.Tech (SEM-V) – AKTU
Time: 3 Hours Total Marks: 70
SECTION A
(Attempt all questions in brief – 2 × 7 = 14 marks)
Q1 (a) What do you mean by degree of redundancy?
Degree of redundancy is defined as the number of additional unknown reactions or internal forces beyond those required for static equilibrium. It represents the extent to which a structure is statically indeterminate.
Q1 (b) Write the assumptions made while developing slope deflection method.
The assumptions are that members are initially straight and prismatic, material follows Hooke’s law, deformations are small, joints are rigid, and axial deformations are neglected.
Q1 (c) What is the effect of temperature change in a cable?
A rise in temperature causes expansion of the cable, increasing sag and reducing tension. A fall in temperature causes contraction, reducing sag and increasing tension in the cable.
Q1 (d) Write different approaches to matrix method.
The matrix method of structural analysis includes flexibility matrix method (force method), stiffness matrix method (displacement method), and finite element method.
Q1 (e) What is restrained structure?
A restrained structure is one in which deformations such as translation or rotation are prevented by supports or boundary conditions, resulting in development of internal stresses.
Q1 (f) Differentiate between plastic modulus and section modulus.
Section modulus is based on elastic stress distribution and is used in elastic design. Plastic modulus is based on plastic stress distribution and is used in plastic design. Plastic modulus is always greater than section modulus.
Q1 (g) Write the limitations of load factor concept.
Load factor concept does not account for serviceability conditions, material imperfections, residual stresses, and deflections. It mainly focuses on collapse load and not on durability or fatigue.
SECTION B
(Attempt any three – 7 × 3 = 21 marks)
Q2 (a) A continuous beam ABCD is loaded as shown. During loading support B sinks by 1 cm. Determine the support moments. Take I = 1600 cm⁴.
The problem is solved using slope deflection equations considering support settlement. Fixed end moments are first calculated due to applied loading. Settlement moments due to sinking of support B are added. Final end moments are obtained by solving simultaneous slope deflection equations at joints A, B, C, and D.
Q2 (b) Determine the centroid and moment of inertia of the given I-section.
The centroid is calculated by dividing the section into flanges and web. Using the principle of moments of areas, the centroidal axis is determined. Moment of inertia is calculated using parallel axis theorem by summing moments of inertia of individual components about the centroidal axis.
Q2 (c) Explain stiffness matrix method.
The stiffness matrix method is a displacement-based method of structural analysis. It relates nodal displacements to forces using stiffness coefficients. The method involves element stiffness matrix formulation, assembly, application of boundary conditions, and solution of simultaneous equations.
SECTION C
Q3 (a) Analyse the frame shown in figure by slope deflection method.
(7 marks)
The analysis is carried out by identifying members, degrees of freedom, and writing slope deflection equations for each member. Fixed end moments due to applied loads are calculated. Boundary conditions are applied and simultaneous equations are solved to determine joint rotations and final end moments.
Q5 (a) A suspension bridge has a cable of span 100 m and dip of 10 m. The cable is stiffened by three hinged stiffening girder. Sketch the influence line diagram for bending moment at quarter span of girder. Determine the maximum moment when a UDL longer than the span of intensity 10 kN/m traverses the span.
(7 marks)
The influence line for bending moment at quarter span is drawn considering unit load moving across the span. The maximum bending moment occurs when the UDL covers the entire region of positive influence line. The maximum moment is calculated by multiplying UDL intensity with area under influence line.
Q6 (a) Analyse the continuous beam shown in figure by flexibility matrix method. Take EI as constant.
(7 marks)
The beam is statically indeterminate. Redundant reactions are identified and flexibility coefficients are calculated. Compatibility equations are written using flexibility matrix. Solving the equations gives redundant forces, from which reactions and bending moments are determined
