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What are the bending moments at ends A and B of uniform fixed beam AB as shown in figure when two concentrated loads acts at 1/3 spans?
When on end of a fixed beam deflects by δ, then the bending moment at deflected end is
If ∑H and ∑V are the algebraic sums of the forces resolved horizontally and vertically respectively, and ∑M is the algebraic sum of the moments of forces about any point, for the equilibrium of the body acted upon.
For equilibrium of any body.
(i) ∑F_{H} = 0
(ii) ∑F_{V} = 0
(iii) ∑M_{Z} = 0
A two hinge arch of span 40 m carries a point load of 62.8 KN at its crown. The Horizontal thrust in the arch is (in KN)
What is the degree of static indeterminacy of the structure shown in figure below?
If a system has more equations of equilibrium than no. of forces, then the system is:
Let D_{s} = static Indeterminacy
D_{s} = R  r
R → no. of unknowns
r → No. of equilibrium equations available
If r > R
D_{s} < 0, system is partially constraintIf
D_{s} > 0, then system is over stiff.
Which of the following material is not used in making trusses?
Concrete is a brittle material and is unable to take tension. In Truss both tension and compression force is available, that’s why concrete is not used in making truss. While metal bars and channels are made of material which have both tensile as well as compressive strength.
Beam are the horizontal members which can transmit the load perpendicular to their longitudinal direction and not in axial direction while truss can transmit the load in axial direction only.
The MullerBreslau principle in structure analysis is used for
Muller Breslau Principle: The MullerBreslau principle states that the ILD for any stress function in a structure is represented by its deflected shape obtained by removing the restrained offered by that stress function and introducing a directly related generalised unit displacement in the direction of that stress function.
The influence line diagram for bending moment at 6 m is shown. The value of the maximum bending moment is:
The value of maximum bending moment is = 200 x 3.6 + 100 x 2.4 = 960 kNm
The degree of static indeterminacy of the pin  jointed plane truss as shown in figure is
D_{s} = m – 2j + r_{e}
m = 23
j = 11
∴ D_{s} = 23 – 22 + 5 = 6
Due to rising temperature in a three hinged arch, induced stress is:
Threehinged arch is a determinate structure and rise in temperature do not produce any stress.
Which of the following equals the number of unknowns to be determined, in stiffness method of structural analysis?
Force method is useful when D_{s} < D_{k}
Displacement method is useful when D_{k} < D_{s}
The unit load method is extensively used in the calculation of deflection of beams, frames and trusses. Theoretically this method can be used to calculate deflections in statically determinate and indeterminate structures. However it is extensively used in evaluation of deflections of statically determinate structures only as the method requires a priori knowledge of internal stress resultants. The unit load method used in structural analysis is derived from Castigliano’s theorem.
The degree of kinematic indeterminacy of the given beam considering axial rigidity is
D_{k} = 3j – r_{e} + r_{r}
= 3 x 4 – 5 + 1 = 8
If members are considered axially rigid
D_{k} = 8 – 3 = 5
Consider the following statements:
The principle of superposition is not applicable when
1. The material does not obey Hooke’s law
2. The effect of temperature changes are taken into consideration
3. The structure is being analysed for the effect of support settlement
Which of these statement (s) is/are correct?
According to the principle of superposition, for a linearly elastic structure, the load effects caused by two or more loadings are the sum of the load effects caused by each loading separately. Note that the principle is limited to:
• Linear material behaviour only;
• Structures undergoing small deformations only (linear geometry).
It is not applicable when:
1. The material does not obey Hooke’s law.
2. The effect of temperature changes are taken into consideration.
3. The structure is being analysed for the effect of support settlement.
Force in the member BC of the truss shown in the given figure is
Clapeyron’s theorem is associated with the analysis of
The given figure shows a portal frame with one end fixed and other hinged. The ratio of the fixed end moments due to side sway will be
Due to sway, the deflection of point B will be equal to that of point C.
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