DESIGN OF STRUCTURE – I (RCE-502)
B.Tech (SEM-V) – AKTU
SECTION A
(Attempt all questions – 2 × 7 = 14 marks)
Q1 (a) Define flexibility and stiffness coefficients.
Flexibility coefficient is defined as the displacement produced at a particular coordinate due to unit load applied at another coordinate, while all other coordinates are restrained. It represents deformation characteristics of the structure.
Stiffness coefficient is defined as the force required at a coordinate to produce unit displacement at that coordinate while all other coordinates are fixed. It represents resistance offered by the structure against deformation.
Q1 (b) Find moment in member OA, OB and OC due to applied moment M at joint O.
When a moment M is applied at joint O connected to members OA, OB and OC, the moment is distributed among the members in proportion to their stiffness. Since stiffness of a member is proportional to EI/L, the moment in each member is obtained by dividing M in the ratio of their stiffness values.
Q1 (c) Find rotation of joint O due to applied moment M. Take EI and length L as constant for all members.
Since all members have equal EI and length L, their stiffness values are equal. Hence the applied moment M is equally distributed. The rotation at joint O is obtained by dividing applied moment by the sum of stiffness of all connected members.
Q1 (d) List three methods of structural analysis using force method concept and three methods using displacement concept.
Force method based approaches include flexibility method, consistent deformation method, and column analogy method.
Displacement method based approaches include slope deflection method, moment distribution method, and stiffness matrix method.
Q1 (e) State lower bound theorem.
Lower bound theorem states that any statically admissible stress distribution that does not violate yield condition anywhere in the structure gives a safe lower bound to the true collapse load.
Q1 (f) What is plastic hinge and plastic moment capacity?
A plastic hinge is a location in a structural member where plastic deformation occurs allowing rotation without any increase in moment.
Plastic moment capacity is the maximum moment a section can resist when it is fully yielded across the entire cross-section.
Q1 (g) State Müller-Breslau’s principle.
Müller-Breslau’s principle states that the influence line for a function is obtained by removing the restraint corresponding to that function and applying a unit displacement in its direction.
SECTION B
(Attempt any three – 7 × 3 = 21 marks)
Q2 (a) Analyze the beam of Fig-3 by slope deflection method.
In slope deflection method, the end moments of beam members are expressed in terms of rotations and displacements of joints. Fixed end moments are first calculated due to applied loads. Slope deflection equations are then written considering joint rotations and support settlements. Finally, equilibrium equations are solved to obtain end moments and reactions.
Q2 (b) Explain stiffness matrix method of analysis.
The stiffness matrix method is a displacement method of structural analysis. It involves forming element stiffness matrices, assembling them into global stiffness matrix, applying boundary conditions, solving for unknown displacements, and then calculating member forces. This method is well suited for computer analysis of large structures.
Q2 (c) Explain flexibility matrix method.
Flexibility matrix method is based on force approach where redundants are chosen and compatibility conditions are applied. Flexibility coefficients relate displacements to applied forces. After solving compatibility equations, internal forces and reactions are obtained.
SECTION C
(Attempt any one from each unit – 7 × 2 = 14 marks)
Q3 (a) A UDL of 2000 kg/m crosses a simply supported girder. Calculate maximum bending moment at a point using influence line.
The influence line for bending moment at the given point is drawn. The maximum bending moment occurs when the UDL covers the portion of the span where the influence line is positive. The maximum bending moment is obtained by multiplying load intensity with the area under influence line over the loaded length.
Q4 (a) Analyze the beam by stiffness matrix method as shown in Fig-8.
Element stiffness matrices are formed for each beam segment. These matrices are assembled into global stiffness matrix. Boundary conditions are applied and joint displacements are calculated. Using these displacements, member end forces and reactions are determined.
Q5 (b) Find shape factor of triangular section.
Shape factor is defined as the ratio of plastic moment to yield moment. For a triangular section, the plastic neutral axis is located closer to the base. By calculating plastic and elastic moments, the shape factor of triangular section is obtained as greater than unity, indicating higher plastic reserve strength.
