Castigliano’s first theorem is applicable
Principle of superposition is applicable when
Please select 2 correct answers
The principle of superposition may be stated as the deflection at a given point in a structure produced by several loads acting simultaneously on the structure can be found by superposing deflections at the same point produced by loads acting individually.
In moment distribution method, the sum of distribution factors of all the members meeting at any joint is always
Moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. The method only accounts for flexural effects and ignores axial and shear effects
The carryover factor in a prismatic member whose far end is fixed is
Carry over factor: - It is a moment developed at the far end due to the unit rotation at the near end (Sign of applied and developed moment is same). COF = Carry over moment / Moment at near end COF = Developed moment (far end) /Applied moment (near end) 1. Far end fixed, then COF = ½ 2. Far end hinged, then COF = 0
The carryover factor in a prismatic member whose far end is hinged is
The moment required to rotate the near end of a prismatic beam through a unit angle without translation, the far end being simply supported, is given by
1. Far end fixed, K = 4EI/L 2. Far end hinged, K = 3EI/L
The moment required to rotate the near end of a prismatic beam through unit angle, without translation ( the far end being fixed ), is given by
If M is the external moment which rotates the near end of a prismatic beam without translation ( the far and being fixed ), then the moment induced at the far end is
The principle of superposition is not applicable when i) The material does not obey Hooke’s law ii) The effects of temperature changes are taken into consideration iii) The structure is being analysed for the effect of support settlement The correct answer is
If the displacement at coordinate i due to unit force at coordinate j is δij, and displacement at coordinate j due to unit force at coordinate i is δji, then according to Maxwell’s Reciprocal theorem,
Maxwell's reciprocal theoremstate that in a linearly elastic structure, the deflection at any point A due to a load applied at some other point B will be equal to the deflection at B when the same load is applied at A
The ordinates of influence line diagram for bending moment always have the dimensions of
An influence line for any given point or section of structure is a curve whose ordinates represent to scale the variation of a function such as shear force, bending moment, deflection etc at a point or section, as the unit load moves across the structure.
If one end of prismatic beam AB with fixed ends is given a transverse displacement Δ without any rotation, then the transverse reactions at A or B due to displacement is
If the sinking of a support of a fixed beam causes the beam to rotate in the clockwise direction, then the moments induced at both the ends of the beam will be
In column analogy method, the area of an analogous column for a fixed beam of span L and flexural rigidity EI is taken as
The degree of static indeterminacy up to which column analogy method can be used is
The deflection at any point of a perfect frame can be obtained by applying a unit load at the joint in
The method of virtual work, or sometimes referred to as the unitload method. Applying a unit load at the point in the direction of which a displacement needs to be calculated.
In the slope deflection equations, the deformations are considered to be caused by i) Bending moment ii) Shear force iii) Axial force The correct answer is
Slope deflection equation give the relationship between bending moment acting on a structures member and displacement of the member at its ends. Mab = Mfab+2EI/L (2θa+θb-3Δ/L)...... Mba = Mfba+2EI/L (2θb+θa-3Δ/L)
The three moments equation is applicable only when
A prismatic beam is simply a beam in which there is a uniform cross section throughout. Three moment equation relates moments at three successive (no discontinuity) supports to applied loading on adjacent spans. Fixed end is replaced by an additional span of zero length.
While using three moments equation, a fixed end moment of a continuous beam is replaced by an additional span of
The Castigliano’s second theorem can be used to compute deflections
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.