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Test: Beams - Mechanical Engineering MCQ


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10 Questions MCQ Test - Test: Beams

Test: Beams for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Test: Beams questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Test: Beams MCQs are made for Mechanical Engineering 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Beams below.
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Test: Beams - Question 1

Which of the following is CORRECT for indeterminate beam condition?

Detailed Solution for Test: Beams - Question 1

A beam is said to be in static equilibrium when the beam is initially at rest and remains at rest when subjected to a system of forces and couples.
Generally, there are 3 equilibrium equations for a planer structure.
The conditions of zero resultant force and zero resultant couple can be expressed as:

where Fx represents forces along the horizontal or x-axis, Fy represents forces along the vertical or y-axis, and Mz represents the sum of moments taken around any point on the beam.
Degree of indeterminacy = Total number of unknown forces - Total number of equilibrium equations

Eg. Statically indeterminate structure

Here, the total number of unknown forces = 7
total number of equilibrium equations = 3
So, the degree of indeterminacy = 7 - 3 = 4, which is greater than zero so it is a statically indeterminate structure.
Eg. Statically determinate structure

Here, the total number of unknown forces = 3
Total number of equilibrium equations = 3
So, the degree of indeterminacy = 3 - 3 = 0, so it is a statically determinate structure.

Test: Beams - Question 2

Consider a beam sustaining a load of "L" kN at its center. Which of the following options gives the maximum bending moment of the given beam? (where I is length of beam)

Detailed Solution for Test: Beams - Question 2

When a simply supported beam is subjected to a point load, L at the center of the length of the beam then there will be the generation of two equal vertical reactions, L/2 at the ends.
By drawing a bending moment diagram of this beam, it is clearly indicated that the maximum bending moment in the beam occurs at the center of beam length and its value is [(L/2) × (l/2)] or L × l/4 kN-m
CASE1

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Test: Beams - Question 3

A cantilever beam is one which is -

Detailed Solution for Test: Beams - Question 3

There are different types of beam:

Overhanging beam:

  • A beam having its end portion extended beyond the support is known as an overhanging beam.
  • A beam may be overhanging on one side or on both sides.

Cantilever beam:

  • A beam fixed at one end and free at the other end is known as a cantilever beam.

Simply Supported Beam:

  • A beam supported at its both ends is known as a simply supported beam.

Fixed beam:

  • A beam whose both ends are fixed is known as a fixed beam.

Continuous beam:

  • A beam supported on more than two supports is known as a continuous beam.

Test: Beams - Question 4

Six fundamental methods of supporting beam are shown below:

Which cases fall under the category of statically indeterminate beams?

Detailed Solution for Test: Beams - Question 4

The beam is a structural member that is subjected to transverse loading to its axis.
Continuous beam:

  • It is a statically indeterminate multi-span beam on hinged support.
  • The end span may be cantilever, may be freely supported or fixed supported.
  • It is a beam having more than 2 supports.


Fixed beam:

  • It is a beam with ends restrained from rotation.
  • The figure shows a fixed beam subjected to uniformly distributed load throughout.
  • It is a statically indeterminate beam on Fixed support.


Overhanging beam:

  • It is defined as a beam that has its one or both ends stretching out past its support.
  • It can have any number of supports.
  • It is a statically determinate multi-span beam on hinged support.


Simply supported beam:

  • A simply supported beam is a type of beam that has pinned support at one end and a roller support at the other end.
  • It is a statically determinate multi-span beam on hinged support.

Propped cantilever beam:

  • The propped cantilever beam is a beam with one end fixed and the other end simply supported.
  • It comes under statically indeterminate beams.

Cantilever beam: 

  • A beam fixed at one end and free at the other end is known as a cantilever beam.
  • It comes under statically determinate beams.

From the above,
Statically determinate beams

  • Cantilever beam
  • Simply supported beam
  • Overhanging beam

Statically indeterminate beams

  • Propped cantilever beam:
  • Fixed beam
  • Continuous beam
Test: Beams - Question 5

A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on motor with respect to center of gravity (CG) of the mobile and the rest of the dimensions of the mobile phone are shown. The mobile is kept on a flat horizontal surface.

Given in addition that the eccentric mass = 2 grams, eccentricity = 2.19 mm, mass of the mobile = 90 grams, g = 9.81 m/s2. Uniform speed of the motor in RPM for which the mobile will get just lifted off the ground at the end Q is approximately.

Detailed Solution for Test: Beams - Question 5
  • When a rotating body is involved then there comes a force which is known as Centrifugal force (Fc)
    It is calculated by using formula
    Fc = mr(ω)2
  • Now in the Question, it is mentioned that end Q is just lifted off the ground. So as it is just lifted off the ground there will be no reaction force from that point.

∴ FBD of mobile

M = mass of mobile
m = eccentric mass
r = eccentricity
Hence, Taking a moment about point P = O
∴ Mg × 0.06 - Fc × (0.09) = 0
∴ 90 × 10-3 × 9.81 × 0.06 = mr(ω)2 × (0.09)
90 × 10-3 × 9.81 × 0.06 = 2 × 10-3 × 2.19 × 10-3 (ω)2 × 0.09
∴ ω2 = 134380.8964
∴ ω = 366.58

∴ N = 3500 rpm

Test: Beams - Question 6

A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of 2L/3 from the hinge so that the rod swings to the right. The horizontal reaction at the hinge is

Detailed Solution for Test: Beams - Question 6


When rod swings to right, Linear acceleration & angular acceleration (∝) comes into picture
Let R = reaction at hinge
Linear acceleration

 ...(1)

Test: Beams - Question 7

A simply supported beam PQ is loaded by a moment of 1 kN-m at the mid-span of the beam as shown in the figure. The reaction forces RP and RQ at supports P and Q respectively are

Detailed Solution for Test: Beams - Question 7

Equilibrium Conditions:

Calculation:
Given:

Now, we know that
Balancing vertical forces by 

RP + RQ = 0 ... (1)
Now,
Taking moment about point 'P'

1 = RQ × 1 ⇒ RQ = 1 kN (upward)
Then, from equation (1), we get
RP = 0 - 1 
∴ Rp = -1 kN = 1 kN (downward)

Test: Beams - Question 8

Impact load is an example of 

Detailed Solution for Test: Beams - Question 8

Load: A load is an external effort acting on the structure.
Uniform loading: The load that is either equal or varies uniformly along the element length is given as uniform load.

Where, UDL = uniformly distributed load, UVL = uniformly variable load
Static loading: Static load is a load that doesn't change over time and there will be no vibrations and no dynamic effects on the member.

Dynamic loading: If the load increases rapidly and changes over time it is known as dynamic loading 
⇒ Impact loading is an example of dynamic loading
Fatigue load: Fatigue loading is primarily the type of loading which causes cyclic variations in the applied stress or strain on a component. Thus any variable loading is basically a fatigue loading. 
Under fatigue load, the material fails due to sudden propagation of cracks and fractures

Test: Beams - Question 9

A simply supported laterally loaded beam was found to deflect more than a specified value. Which of the following measures will reduce the deflection?

Detailed Solution for Test: Beams - Question 9

From differential equations of elastic curve

Where y = deflection of beam.
As the I = Area moment increases, the deflection will reduce.

Test: Beams - Question 10

The area moment of inertia of a square of size 1 unit about its diagonal  is

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