A fixed beam of length L with central point load P has the fixed end moment equal to:
For fixed beam with central point load, fixed end moment = PL/8 and maximum deflection = PL³/(192EI).
In virtual work method, if a unit load is applied instead of actual load, the virtual displacement is equal to:
Virtual work principle: Work done by actual loads through virtual displacements equals work by virtual loads through actual displacements.
The stiffness matrix in matrix method of structural analysis represents:
[K]{D} = {F}, where stiffness matrix K relates displacements D to forces F. K represents member/structure stiffness.
In a three-hinged arch, the additional hinge at crown provides:
Three-hinged arch has 4 reactions with 3 global + 1 local equilibrium equation at crown, making it statically determinate (DSI=0).
For a continuous beam with equal spans and equal loads, the negative moment at interior support is maximum at:
For symmetrical continuous beam with equal spans and loads, negative moments at all interior supports are equal.
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In slope-deflection method, the fixed-end moment for a fixed beam with UDL w over length L is:
Fixed-end moment for fixed beam with UDL = wL²/12 at each end (opposite signs).
The principle of virtual displacements is applicable to:
Virtual work principle applies universally to all structures, both determinate and indeterminate, and rigid/deformable bodies.
What is the water-cement ratio for M20 grade concrete as per IS 456:2000?
For M20 concrete, the maximum water-cement ratio is 0.55 to achieve the specified 28-day compressive strength.
What is the recommended slump for RCC columns according to IS 456:2000?
For RCC columns, the recommended slump is 25-50 mm to ensure adequate compaction and workability.
Hydration of cement produces which of the following as main products?
CSH (Calcium Silicate Hydrate) and CH (Calcium Hydroxide) are the main hydration products that give strength to concrete.
What is the minimum concrete cover for reinforcement in foundations as per IS 456:2000?
IS 456:2000 specifies 50 mm minimum concrete cover for reinforcement in submerged/buried foundations.
Which of the following factors increases the compressive strength of concrete?
Pozzolanic materials like fly ash and silica fume react with calcium hydroxide to improve strength and durability.
What is the typical strength gain pattern of concrete in the first 28 days?
Concrete gains approximately 40-50% strength in 7 days due to rapid hydration, then strength gain slows down gradually.
What is the effect of adding admixtures like retarders in concrete?
Retarders delay the setting time of concrete, allowing more time for placement and compaction in large structures.
What is the recommended curing period for concrete in normal conditions?
IS 456:2000 recommends minimum 14 days of moist curing for normal Portland cement in normal temperature conditions.
In a two-hinged arch, the number of unknown reactions is:
Two-hinged arch has 2 supports (each with 2 reactions) = 4 unknowns total (horizontal and vertical at each hinge).
The influence line for a reaction at support A of a simply supported beam AB is:
Influence line for reaction at A is triangular, varying from 1 at A to 0 at B, representing the reaction at A due to unit load.
In matrix stiffness method, the element stiffness matrix for a truss member is derived using:
Element stiffness matrix is derived by applying unit displacements at nodes and calculating corresponding forces (unit displacement method).
The carry-over factor in slope-deflection method for a member with far end fixed is:
Carry-over factor = 0.5 for both fixed and pinned end conditions in slope-deflection method.
In moment distribution method, the distribution factor for a member is proportional to:
Distribution factor = (stiffness of member)/(sum of stiffness of all members at joint). DF ∝ stiffness (4EI/L).
