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WorksheetsMechanics of Structures Quiz
Total questions: 119
Worksheet time: 2hrs 15mins
Which of the following is most required when using Mohr’s area moment method?
It can be applied to beams with point loads
It requires careful evaluation of areas and centroids of M/EI diagrams
It accounts for shear force effects
It can be used for a variety of beam supports
The unit of slope in beam deflection problems is:
Metre
Radian
Newton per metre
Dimensionless
If the slope at a point is known, the deflection can be obtained by
Differentiating slope with respect to $x$
Integrating slope with respect to $x$
Equating slope with shear force
Multiplying slope with span length
Flexural rigidity of a beam is defined as:
Product of Young’s modulus (E) and area (A)
Product of Young’s modulus (E) and moment of inertia (I)
Ratio of load to deflection
Ratio of bending stress to strain
Which one of the following is NOT an assumption in applying Mohr’s theorems?
Beam material obeys Hooke’s law
Deflections are small compared to span length
Shear deformation is neglected
Load is always uniformly distributed
A simply supported beam subjected to a central point load will have its deflected shape as:
Symmetric curve with maximum deflection at mid-span
Straight line throughout the span
Symmetric curve with maximum slope at mid-span
Antisymmetric curve with maximum deflection at the supports
Deflection of a beam at any point is:
Distance between maximum bending moment and shear force
Tangential angle of the slope
Vertical displacement of the neutral axis relative to original position
Rotation of cross-section about neutral axis
A cantilever of length L subjected to a uniformly distributed load w (per unit length). Which of the following best describes the deflected shape?
Straight line inclined uniformly
Circular arc with radius proportional to w
Parabolic curve with maximum deflection at free end
Cubic curve with maximum deflection at free end
For a cantilever beam of length $L$ carrying a point load $P$ at the free end, the maximum deflection is:
For a simply supported beam under UDL $w$, the maximum deflection at mid-span is:
Which one of the following beams will show zero slope at both supports?
Cantilever beam
Simply supported beam
Fixed beam
Propped cantilever beam
Stiffness of a beam is defined as:
Product of load and deflection
Ratio of shear force to span
Ratio of load applied to deflection produced
Ratio of bending moment to slope
The deflection at mid-span of a simply supported beam with a central point load can be found by Mohr’s theorem as:
Moment of $M/EI$ area about the support
Area of bending moment diagram
Moment of $M/EI$ area about the mid-span
Double integration of load equation
A cantilever beam carrying a UDL over the entire span $L$, the maximum slope at the free end is
$wL^3/ 3 EI$
$wL^3/ 6 EI$
$wL^2/ 2 EI$
$wL^4/8 EI$
The stiffness of a beam is generally defined as
Resistance against bending moment
Load required to produce unit deflection
Product of load and span length
Ratio of span to depth
Among beams made of the same material, with identical cross-section and subjected to the same load, which beam will exhibit the greatest stiffness?
Maximum span length
Least span length
Hinged supports
Roller supports
Deflection of a beam at a given section refers to
The horizontal displacement of supports
The bending stress at that section
The rotation of the cross-section
The vertical distance moved by the neutral axis relative to its original position
For a simply supported beam under UDL, the slope at supports using Mohr’s theorem is obtained from:
Total area of $M/EI$ diagram
Moment of the $M/EI$ diagram about support
Centroid of shear diagram
Integration of deflection curve
The slope at a section of a beam is defined as
The angle between the tangent to the elastic curve and the vertical axis
The ratio of deflection to length
The angle between the tangent to the elastic curve and the horizontal axis
The maximum deflection of the beam
If the flexural rigidity of a beam is doubled, the deflection under a given load will:
Remain same
Become half
Become double
Become one-fourth
The maximum deflection of a simply supported beam of span $L$ with a central point load $P$ is:
Which of the following correctly represents the relation between deflection $y$, slope $ heta$, and bending moment $M$?
According to the First Moment-Area Theorem, the change in slope between two points of a beam is equal to
Centroidal distance of $M/EI$ diagram
Maximum ordinate of the bending moment diagram
Deflection at the midpoint of the span
Area of the $M/EI$ diagram between the two points
For a cantilever beam of length $L$ under UDL $w$, the maximum deflection at the free end is:
Flexural rigidity of a beam is defined as:
Product of modulus of elasticity and moment of inertia
Ratio of modulus of elasticity (E) to moment of inertia (I)
Ratio of bending stress to strain
Product of bending stress and strain
For a cantilever beam with a point load at its free end, the slope is maximum at:
Fixed support
Free end
At the middle of the span
At quarter span from the fixed end
The sum of fixing end moments in a fixed beam carrying a central point load $P$ is:
For a fixed beam of span $L$ carrying vertical loads, the number of unknown reactions is:
One major structural advantage of a fixed beam is:
Maximum bending moment is reduced compared to a simply supported beam
Deflection increases at mid-span
It becomes statically determinate
Shear force vanishes at ends
In comparing free BMD (simply supported) and fixed BMD for the same loading condition, the fixed beam shows:
Equal maximum bending moment
Higher mid-span bending moment
Smaller maximum bending moment
Larger shear at mid-span
In structural analysis, a hogging moment is generally taken as
Positive
Negative
Zero
Always variable
Where does maximum positive bending moment occur in a fixed beam with UDL?
At the supports
At the points of contraflexure
At quarter span from each support
At the center of the beam
For a fixed beam of span $L$ carrying a central point load $P$, the fixing end moment at each support is
A fixed beam is defined as a beam in which:
Both ends are free to rotate but not translate
Both ends are restrained from rotation as well as translation
One end fixed, other free
One end hinged, other free
What does the free bending moment diagram of a fixed beam primarily represent?
The distribution of shear forces along the beam length
The points of maximum stress in the beam
The deflection shape of the beam under loading
The variation of bending moments along the length of the beam due to applied loads
Which statement is correct regarding sagging and hogging moments?
Sagging = compression at bottom fibers
Hogging = compression at bottom fibers
Sagging = concave downwards
Hogging = concave upwards
A fixed beam is statically:
Determinate
Indeterminate to degree one
Indeterminate to degree two
Indeterminate to degree three
For a fixed beam carrying a central point load $P$, the bending moment at the supports will be:
Hogging
Sagging
Zero
Variable sign
For a fixed beam under UDL, the shape of the BMD is:
Rectangular
Parabolic with hogging at supports and sagging at mid-span
Triangle with hogging at supports and sagging at mid-span
Trapezoidal
Which of the following is an advantage of a fixed beam as compared to a simply supported beam?
It reduces the maximum bending moment at the center
It is less stiff and strong
Its ends are free to rotate
It has higher maximum deflection at center
For a fixed beam under uniform load, the points of contraflexure are located:
Exactly at the support
At mid-span
Between mid-span and supports
Nowhere in the span
In a bending moment diagram, the point of contraflexure is identified as:
Point of maximum bending moment
Point of maximum shear
Point where slope of elastic curve = 0
Point where bending moment = 0 between hogging and sagging zones
In a fixed beam subjected to a uniformly distributed load, how is the point of contraflexure best described?
It is the point where the beam has maximum shear force
It is the point where the bending moment is zero and changes sign from positive to negative (or vice versa)
It is always located at the center of the beam
It is the support location of the beam
Compared to a simply supported beam, a fixed beam carries the same load with:
Smaller deflection
Larger deflection
Same deflection
Zero deflection
A bending moment that causes the beam to bend in a concave upward shape is called:
Sagging moment
Hogging moment
Shear force
Neutral axis moment
In a fixed beam subjected to downward loads, what do the terms "sagging" and "hogging" represent?
Sagging refers to negative bending moment, hogging refers to positive bending moment
Sagging refers to positive bending moment (beam curves downward in the span), hogging refers to negative bending moment (beam curves upward at supports)
Sagging and hogging both refer to zero bending moment
Sagging and hogging refer to shear force only
For a fixed beam of span $L$ under a uniformly distributed load $w$, the fixing end moment at each support is:
For a given span and load, fixed beams are
Uneconomical because they require heavier sections
Less economical than simply supported beams in terms of material usage
More economical than simply supported beams due to reduced bending moments
Equally economical as simply supported beams
In the area moment method, the slope at a support of a fixed beam is:
Always zero
Equal to $M/EI$
Equal to deflection at that point
Proportional to span length
What is the degree of static indeterminacy for a fixed beam?
Total reactions plus equilibrium equations
Total reactions minus equilibrium equations
Only vertical reactions
Number of spans times unknowns
A two-span continuous beam with both ends fixed and one intermediate support has a degree of indeterminacy equal to:
Which among the following option is an example for Determinate structure?
Simply supported beam
Fixed beam
Propped cantilever beam
Continuous beam
The degree of indeterminacy of a three-span continuous beam fixed at both ends is:
What is the main structural advantage of a continuous beam over a simply supported beam?
Easier construction
Lower maximum bending moments
No need for supports
Simple analysis
The degree of indeterminacy of a continuous beam depends primarily on:
Number of spans and type of supports
Cross-section only
Loading type only
Material property only
In practice, Clapeyron’s theorem is most useful for:
Exact analysis of complex indeterminate structures
Approximate estimation of deflections
Quick determination of support moments in continuous beams
Analysis of plastic hinges
In Clapeyron’s theorem, if both end supports are simply supported (i.e., $M_A=M_C=0$), the central support moment $M_B$ depends on:
Only loading type
Only span lengths
Both loading type and relative span lengths
Neither, it is always zero
If a continuous beam has $n$ spans and is supported on rigid supports, the degree of indeterminacy is:
n−1
2n
$n$
n+1
Which of the following structures behaves similarly to a continuous beam?
Cantilever balcony
Simply supported roof truss
Suspension bridge cable
Railway track on sleepers
Which of the following is an advantage of continuous beams over simply supported beams?
Larger mid-span deflections
Higher maximum bending moments
Reduction in maximum bending moment and deflection due to continuity
Less redundancy in structure
In a two-span continuous beam with central load in one span only, the deflection in the unloaded span will be:
Zero
Downward (sagging)
Upward (hogging)
Same as loaded span
For a two-span continuous beam with equal spans under uniformly distributed load $w$, but with both ends fixed, the bending moment at the central support (from Clapeyron’s theorem) is:
For a two-span continuous beam under equal loads, the maximum sagging deflection occurs:
At mid-span of each span
At both supports simultaneously
At the central support
At quarter-span
Which real-life structure is best modeled as a continuous beam?
Cantilever signboard
Overhead transmission line
Bridge deck supported on multiple piers
Ladder resting against a wall
The static indeterminacy of a continuous beam with three supports is:
The elastic curve (deflected shape) of a two-span continuous beam under uniform load is
Single symmetric sagging curve
Sagging in spans with a hogging region at intermediate support
Hogging in spans with sagging only at supports
Flat without curvature
Which among the following option is an example for indeterminate structure?
Simply supported beam
Over Hanging beam
Cantilever beam
Continuous beam
A continuous beam with three supports (two spans) is statically:
Determinate
Indeterminate to degree 1
Indeterminate to degree 2
Indeterminate to degree 3
Compared to a simply supported beam, a continuous beam is
Unstable in nature
Never used in practice
Less economical
More economical in material usage
Clapeyron’s theorem of three moments is applicable to:
Simply supported beams only
Cantilever beams only
Continuous beams
Overhanging beams only
Clapeyron’s theorem fails to give correct results if:
Beam has variable $EI$ in spans
Load is triangular
Supports are rigid
Beam has more than 3 spans
The moment distribution method becomes inaccurate when:
Support settlements occur
More than three spans exist
End supports fixed
EI is constant for all spans
In continuous beams, redistribution of moments leads to:
Increase in maximum deflection
Increase in shear force at mid-span
Economy in reinforcement
Loss of stability
A continuous beam is defined as
A beam extending over more than two supports
A beam fixed at one end and free at the other
A beam supported only at one end
A beam supported at both ends only
For a continuous beam with spans $L_1$ and $L_2$, the three-moment equation relates:
Shear forces at three successive supports
Bending moments at three successive supports
Deflections at three successive supports
Load intensities on two successive spans
The degree of indeterminacy of a continuous beam increases with
Increase in number of spans
Reduction in number of supports
Removal of fixity
Shortening the span
The distribution factor at a joint is equal to:
The deflected shape of a non-sway portal frame under symmetric vertical loading is:
Columns bend outward, beam sags
Columns bend inward, beam hogs
Columns remain vertical, beam sags
One column sways outward, the other inward
The sign convention in moment distribution method assumes clockwise moments at the joint as:
Positive
Negative
Zero
Dependent on support type
A non-sway frame is one in which:
Columns are infinitely rigid
Lateral displacement of joints is prevented
Vertical loads are not considered
Members are pin-connected
Which of the following is a distinguishing feature of a portal frame?
All joints are hinged
Columns are always circular
Rigid connections between beams and columns
It is always sway-prone
During moment distribution, the process of transferring a portion of moment to the far end of a member is called
Deducting
Distribution
Balancing
Conjugation
Relative stiffness of a beam is defined as:
Ratio of carryover factor to stiffness factor
Ratio of stiffness of member to total stiffness at the joint
Ratio of stiffness of one member to another at the same joint
Ratio of distribution factor to stiffness
The sum of distribution factors at a joint in moment distribution method is always equal to:
If three members of stiffnesses $2EI/L$, $3EI/L$, and $EI/L$ meet at a joint, the distribution factor of the second member is:
0.25
0.375
0.5
0.6
Which of the following will generally cause sway in a portal frame?
Symmetrical vertical loading
Equal stiffness of columns
Lateral loading or unequal column stiffness
Fixed supports at both ends
For a beam with both ends fixed, the stiffness factor at each end is:
The moment distribution method is primarily used for analyzing:
Statically determinate beams
Indeterminate beams and frames
Trusses
Trusses
If two beams of equal stiffness meet at a joint, their distribution factors are:
1 and 0
0.25 and 0.75
0.5 and 0.5
0.6 and 0.4
Which of the following is TRUE regarding carryover factors?
They are always positive
They can be zero depending on end condition
They are always equal to stiffness factor
They are independent of end conditions
In moment distribution, which of the following best represents the iteration process?
Moments are distributed once and carried over only once
Moments are repeatedly distributed and carried over until balance is achieved
Only carryover is applied without distribution
Equilibrium is forced at supports without considering stiffness
The carryover factor for a prismatic member with one end fixed and the other end hinged is:
In moment distribution method, the carryover factor for a prismatic beam with both ends fixed is:
In a fixed–pinned beam analyzed by moment distribution, the stiffness factor at the fixed end is:
In moment distribution, an unbalanced moment at a joint is first:
Carried over to the far end
Distributed among connected members
Eliminated by sway correction
Converted into shear force
The stiffness of a member in moment distribution is proportional to:
If a column has effective length 3 m and radius of gyration 100 mm, its slenderness ratio is:
10
20
30
40
Which of the following end condition gives maximum load-carrying capacity for a column of given material and cross-section?
Both ends hinged
Both ends fixed
One end fixed, one end free
One end fixed, one end hinged
For a column with one end fixed and the other hinged, effective length is approximately:
0.7L
0.5L
1L
2L
Higher slenderness ratio indicates that the column is more prone to:
Crushing failure
Buckling failure
Shear failure
Fatigue failure
Euler’s formula shows that the critical load is inversely proportional to:
Young's Modulus
Moment of inertia
Square of effective length
Radius of gyration
A column with both ends fixed has a critical load compared to a similar column hinged at both ends which is:
Equal
Two times greater
Four times greater
Half
Which of the following conditions is critical for a long axially loaded column?
Slenderness ratio < 12
Slenderness ratio > 80
Cross-sectional area is large
Effective length is very small
For a long column, as the effective length increases, the critical buckling load
Increases
Decreases
Remains constant
Becomes zero
If eccentricity of load is zero, the stress in a short column is:
Bending stress
Pure axial compressive stress
Shear stress
Torsional stress
For a short axially loaded column, the stress distribution over the cross-section is assumed to be:
Uniform
Linear
Parabolic
Circular
The effective length of a column depends on:
Load intensity
Load intensity
End conditions
Cross-section shape
The main difference between a column and a strut is:
Column is always vertical, strut may be inclined
Column carries axial compression, strut carries bending
Column is slender, strut is short
Column is tensioned, strut is compressed
Which of the following statements is correct?
All columns are struts, but all struts are not columns
All struts are columns, but all columns are not struts
Columns and struts are the same
A strut always resists tensile load
Sketch the deflected shape of a simply supported beam under a uniformly distributed load
Define slope
What is meant by deflection of a beam?
Define flexural rigidity and stiffness of a beam.
What is the degree of indeterminacy of a fixed beam?
Do fixed beams generally have points of contra-flexure? Why?
State one advantage of a fixed beam.
Describe the general deflected shape of a continuous beam under uniformly distributed load.
Why is a continuous beam considered statically indeterminate?
Give one real-life application where continuous beams are preferred.
