AMIE Study Circle Blog

Structural Analysis

 1. Applying the static equations ∑H = 0, ∑V = 0 and ∑M = 0 to a determinate structure, we may determine (a) supporting reactions only (b) shear forces only (c) bending moments only (d) all the above* Answer: For statically determinate structure, it is possible to determine support reactions. shear force and bending moment by using equations of static equilibrium.  2. The equivalent length of column of length L having both ends hinged is (a) 2L (b) L* (c) L/2 (d) L/√2 Hint:  3. A fillet weld is termed as (a) mitre weld (b) concave weld (c) convex weld (d) all the above* Hint: A gentle curve pointing away from the hypotenuse means a concave weld is required, a straight line parallel with the hypotenuse calls for a flat faced weld, and a gentle curve towards the hypotenuse calls for a convex weld . 4. The strain energy stored in a spring when subjected to greatest load without being permanently distorted, is called (a) stillness (b) proof resilience* (c) proof stress (d) p...

Answer the following (4 marks each). Explain various components of gantry girder through neat sketches. The plate girder consists of the following components:    The web plate     Flange plate (addition of cover plate curtailed at proper sections)     Stiffeners like bearing stiffeners, longitudinal stiffeners, and intermediate stiffeners     Splices for flange plate and web plate     End connections Generally, gantry girders are supported on brackets connected to columns for lighter loads and are directly supported on columns for heavier loads.  A suitable seat is fabricated to support and connect the bottom flange of the gantry girder. The gantry girder is connected to the column near the top flange to provide lateral support and torsional restraint by channel sections.    Some of the typical sections are: Advantages of HSFG bolts over bearing bolts. The high strength bolts are also called high streng...

Answer the following (10 x 2) What for Castigliano’s first theorem is used? Castigliano’s first theorem: The first partial derivative of the total internal energy (strain energy) in a structure with respect to any particular deflection component at a point is equal to the force applied at that point and in the direction corresponding to that deflection component. This first theorem is applicable to linearly or non-linearly elastic structures in which the temperature is consta nt and the supports are unyielding. It is given as ∂U/∂Δ i  = P i Discuss the concept of indeterminacy for steel structures. A structure that cannot be analysed by using equations of equilibrium only is called a  statically indeterminate structure,  e.g., fixed beams, continuous beams, propped cantilevers.  To analyse indeterminate structures, apart from using equations of equilibrium, one has to determine the various deformations and make use of compatibility conditions.  Indeterminate str...

Answer the following (10 x 2) State the conditions for a stable determinate structure. The structures are grouped into statically determinate and statically indeterminate structures. A structural system that can be analysed by using equations of statical equilibrium only (∑F x  = 0, ∑F y  = 0 and ∑M=0) is called a statically determinate structure , e.g., beams o r trusses with both ends simply supported, one end hinged and another on rollers and the cantilever type.  A structure that cannot be analysed by using equations of equilibrium only is called a statically indeterminate structure, e.g., fixed beams, continuous beams, propped cantilevers. To analyse indeterminate structures, apart from using equations of equilibrium one has to determine the various deformations and make use of compatibility conditions.  Indeterminate structures arc also called redundant structures. When do you go for the method of sections? In the  section method , the truss is...

Answer the following (10 x 2) Define the Distribution factor used in the Moment Distribution Method. Consider a joint in a structure where two or more members meet. If an external moment M is applied to such a joint, the joint undergoes a rotation θ. Since all the members meeting at this joint undergo the same rotation θ. the applied moment M is distributed to each of the ends of the members according to their relative stiffness values. The factor by which the applied moment is multiplied to obtain the end moment of any member is known as the distribution factor (D.F.). State Castigliano’s Second Theorem. Castigliano’s Second Theorem: If a linearly elastic structure is subjected to a set of loads, the displacement of any load in its direction is equal to the partial derivative of the total strain energy with respect to that load. P i  and D i  can also be the moment and the angular rotation respectively. State relationship between Flexibility and Stiffness matrix The element s...

Fill in the blanks with appropriate words (5 x 2) 1. The simply supported beam of length L loaded with a uniformly distributed load of W per unit length. The maximum deflection will be ⸺ Answer: 5WL⁴/384EI 2. Redundant frames may be analysed by ⸺ Answer: Castigliano's second theorem. Castigliano’s second theorem: The first partial derivative of the total internal energy in a structure with respect to the force applied at any point is equal to the deflection at the point of application of that force in the direction of its line of action. The second theorem of Castigliano is applicable to linearly elastic structures with constant temperature and unyielding supports. 3. A three-hinged semicircular arch of radius "r" is subjected to a uniformly distributed load of‘ W per unit length on the whole span. The horizontal thrust will be given by ⸺ Answer: Wr/2 ∑M A  = 0 V B  X 2r - W X r X 2r = 0 V B  = W x r ∑V = O V A  = V B  = W x r M C  = 0 V B  x r — ...

Multiple Choice Questions (10 x 2) 1. Thickened part of a flat slab over its supporting column, is technically known as (a) Drop panel* (b) Capital (c) Column head (d) None of these 2. Side face reinforcement shall be provided in the beam when the depth of the web in a beam exceeds (a) 50 cm (b) 75 cm (c) 100 cm (d) 120 cm 3. For the initial estimate for a beam design, the width is assumed (a) 1/15th of span (6) 1/20th of span (c) 1/25th of span (d) 1/30th of span 4. In a slab, the pitch of the main reinforcement should not exceed its effective depth (a) Three times (b) Four times (c) Five times (d) Two times 5. The Young’s modulus of elasticity of steel is (a) 150 KN/mm² (b) 200 KN/mm² (c) 250 KN/mm² (d) 275 KN/mm² 6. Which of the following methods of structural analysis is a force method? (a) Slope deflection method (b) Column analogy method (c) Moment distribution method (d) None of the above 7. If in a rigid-jointed space frame. (6m + r) < 6j, then the frame is (a) Unstable (b) ...

Answer the following (4 x 5) Explain various components of the Plate girder through a neat sketch. The vertical plate of the plate girder is termed a web plate . The angles connected at the top and bottom of the web plate are known as flange angles . The horizontal plates connected with the flange angles are known as flange plates or cover plates . The web plate, flange angles and flange plates are shown in the following figure. The bearing stiffeners, intermediate stiffeners and horizontal stiffeners used with the plate girder are shown in the following figure. Compare HSFG bolts and bearing bolts. The high strength bolts are also called high strength friction grip bolts. Briefly, these are called HSFG bolts. The high strength friction grip bolts have many advantages over rivets.  Whereas the rivets are subjected to shear and bearing stresses, the bolts are subjected to uniform tensile stresses only.  The high strength friction grip bolts have higher fatigue stren...