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DEFLECTION OF BEAMS

Total questions: 58

Worksheet time: 4hrs 21mins

Name
Class
Date
1.

A mathematical property of a cross section (measured in inches) that gives important information about how that cross-sectional area is distributed about a centroidal axis:

a)

Centroid Principles

b)

Moment of Inertia

c)

Modulus of Elasticity

d)

Beam Deflection

2.

The ratio of the increment of some specified form of stress to the increment of some specified form of strain. Also known as coefficient of elasticity, elasticity modulus, elastic modulus:

a)

Centroid Principles

b)

Moment of Inertia

c)

Modulus of Elasticity

d)

Beam Deflection

3.

Object’s center of gravity or center of mass.

a)

Centroid Principle

b)

Moment of Inertia

c)

Modulus of Elasticity

d)

Beam Deflection

4.

Beam A and B are the same material and same dimensions. What distinguishes beam A from beam B?

a)

Beam A will have a greater resistance to bending because it has a lower moment of inertia.

b)

Beam A will have a greater resistance to bending because it has a higher moment of inertia.

c)

Beam B will have a greater resistance to bending because it has a lower moment of inertia.

d)

Beam B will have a greater resistance to bending because it has a higher moment of inertia.

5.

Correct formula for calculating beam deflection:

a)
b)
c)
d)
6.

Given the information above, calculate the beam deflection for Beam A:

a)

.12 inches

b)

1.39 inches

c)

.53 inches

d)

.24 inches

7.

In the formula above, how to do read the 'Σ' symbol?

a)

Average of

b)

Product of

c)

Sine of 

d)

Sum of

8.

A rectangular beam of length l supported at its two ends carries a central point load W. The maximum deflection occurs

a)

at the ends

b)

at l/3 from both ends

c)

at the centre

d)

none of these

9.

The elastic limit of specific steel is 200 x 106 Pa. Find the minimum radius a steel wire can have (in millimeters) to support a 7,500 N weight without exceeding its elastic limit.

a)

3.5 mm

b)

4.2 mm

c)

1.5 mm

d)

2.9 mm

e)

10.5 mm

10.

An aluminum sample with a diameter of 1.0 in has been tensile tested. Calculate the engineering stress for an applied load of 4020 lbs.

a)

5,118 psi

b)

3,660 psi

c)

7,960 psi

d)

1,990 psi

e)

2,542 psi

11.

Using the stress-strain curve above, what is the yield strength for aluminum?

a)

≈ 130 Mpa

b)

≈ 250 Mpa

c)

≈ 230 Mpa

d)

≈ 200 Mpa

12.

What does point A, B, D, E represent, respectively?

a)

A: Yield Strength, B: Modulus of Elasticity, D: Tensile Strength, E: Strength at Failure

b)

A: Modulus of Elasticity, B: Yield Strength, D: Tensile Strength, E: Strength at Failure

c)

A: Modulus of Elasticity, B: Yield Strength , D: Tensile Strength, E: Strength at Failure

d)

A: Yield Strength, B: Modulus of Elasticity, D: Strength at Failure, E: Tensile Strength

13.

Which of the following are items that do not affect the tensile strength of a member?

a)

cross-sectional area

b)

length

c)

material

d)

shape

e)

density

14.

Compare the maximum deflection distance for two boards made of yellow pine with a cross-section of 3 in. by 5 in.


If the two boards experience 1000 N point load at the center of the beam, but one board is 3 times longer, then which of the following is true?

a)

The longer board deflects 27 times more.

b)

The longer board deflects 9 times more.

c)

The longer board deflects 3 times more.

d)

The shorter board deflects 8 times more.

15.

Using the stress-strain curves provided, which of the two materials experiences more plastic deformation?

a)

Material #1

b)

Material #2

16.

Using the stress-strain curves provided above, which of the two materials shown is more brittle?

a)

Material #1

b)

Material #2

17.

What does the Moment of Inertia describe?

a)

An objects stiffness related to its shape

b)

An objects stiffness related to its chemical properties

c)

An objects rotation because of inertia

d)

An objects rotation because of force

18.

What does the Modulus of Elasticity describe?

a)

An objects stiffness based on its shape

b)

An objects stiffness based on its chemical properties

c)

An objects rotation because of inertia

d)

An objects rotation because of force

19.

Why does a beam's orientation change it's Moment of Inertia? (Choose the BEST option)

a)

You are changing what the measured Height is, which heavily impacts Inertia Calculations

b)

You are changing the measured Base, which heavily impacts Inertia Calculations

c)

You are changing the beam's length, which heavily impacts Inertia Calculations

d)

Beam orientation doesn't matter, the Moment of Inertia stays the same.

20.

Describe the relationship between the maximum beam deflection and the length of the beam. Are the two directly related? Inversely related? Not related?

a)

Directly Related: As the length of the beam increases, so does the maximum beam deflection.

b)

Inversely Related: As the length of the beam increases, the maximum beam deflection decreases, and vice versa.

c)

Not related

21.

The ratio of stress and strain is called the...

a)

plastic deformation

b)

ductility

c)

modulus of elasticity

d)

resistance to rupture

22.

Point C represents what on the stress-strain curve?

a)

Elastic Limit

b)

Ultimate Tensile Strength

c)

Necking

d)

Failure

23.
Once the material goes past the elastic limit it can never go back to its original shape.
a)
True
b)
False
24.
The sum of all forces acting on an object and direction
a)
Contact Force
b)
Balanced Force
c)
Unbalanced Force
d)
Net Force
25.
A free-body diagram represents all of the following except
a)
forces as vectors
b)
forces exerted by the object.
c)
the object
d)
forces exerted on the object.
26.

What units is Modulus of Elasticity measured in?

a)

in4

b)

in2

c)

psi

d)

lbf

27.

What units is Moment of Inertia measured in?

a)

in4

b)

psi

c)

in2

d)

lbf

28.

Statics is

a)

when forces act on a body at rest

b)

study of forces & effects on systems in uniform motion

c)

the same as Center of Mass

d)

A twisting effort about a point when a force is applied

29.

Object’s center of gravity or center of mass.

a)

Centroid Principle

b)

Moment of Inertia

c)

Modulus of Elasticity

d)

Beam Deflection

30.

Beam A and B are the same material and same dimensions. What distinguishes beam A from beam B?

a)

Beam A will have a greater resistance to bending because it has a lower moment of inertia.

b)

Beam A will have a greater resistance to bending because it has a higher moment of inertia.

c)

Beam B will have a greater resistance to bending because it has a lower moment of inertia.

d)

Beam B will have a greater resistance to bending because it has a higher moment of inertia.

31.
What is the centroid of this object? (x,y)
a)
0.375 in, 0.25 in
b)
0.25 in, 0.375 in
c)
0.25 in, 0.25 in
d)
0.25 in, 0.167 in
32.

What is the centroid of this object?

a)

x = 2.71 in, y = 2.71 in

b)

x = 3 in, y = 3 in

c)

x = 2.75 in, y = 2.75 in

d)

x = 3.14 in, y = 3.14 in

33.

What is TRUE about Moment of Inertia (I)?

a)

In general, a higher moment of inertia produces a greater resistance to deformation.

b)

In general, a lower moment of inertia produces a greater resistance to deformation.

c)

In general, a higher moment of inertia produces a reduced resistance to deformation.

34.

The formula to calculate the x-bar of this shape.

a)

B2\frac{B}{2}

b)

B3\frac{B}{3}

c)

4r3π\frac{4r}{3\pi}

d)

rr

35.

The formula to calculate the x-bar of this shape.

a)

B2\frac{B}{2}

b)

B3\frac{B}{3}

c)

4r3π\frac{4r}{3\pi}

d)

rr

36.

The formula to calculate the y-bar of this shape.

a)

B2\frac{B}{2}

b)

B3\frac{B}{3}

c)

4r3π\frac{4r}{3\pi}

d)

rr

37.

The formula to calculate the x-bar of this shape.

a)

B2\frac{B}{2}

b)

B3\frac{B}{3}

c)

4r3π\frac{4r}{3\pi}

d)

rr

38.

 I = bh312I\ =\ \frac{bh^3}{12}  

Calculate the moment of inertia of this beam.  Round your answer to the nearest whole number and do not include units.



(a)  

39.

Using the equation for the moment of inertia above, find the base of a piece of wood that has moment of inertia 21 and height 5.5.

a)

1.5

b)

2

c)

1

d)

15

40.

Does the top plank or bottom plank seem to have a higher modulus of elasticity?

a)

Top plank

b)

Bottom plank

c)

They are the same

41.

The centroid of an object is...

a)

its center of gravity or center of mass

b)

its center point

c)

its balancing point

42.

TRUE or FALSE: in symmetrical objects, the centroid is determined by an object's line of symmetry.

a)

True

b)

False

43.

While using slope deflection method, in which direction is moment taken as positive?

a)

Depends upon loading

b)

Anti-clockwise

c)

Depends upon case

d)

Clockwise

44.

Fixed end moment formula for UDL load

a)

WL2/12

b)

WL2/8

c)

WL2/6

d)

WL2/10

45.

fixed end moment formula for point load at center of the span

a)

WL2/12

b)

WL/8

c)

WL2/10

d)

WL2/10

46.

Based on moment equation given, determine the value of θB and θC

a)

θB = -45/EI θC = 45/EI

b)

θB = 45/EI θC = -45/EI

c)

θB = -90/EI θC = 90/EI

d)

θB = 90/EI θC = -90/EI

47.

In simply supported beam, where is maximum deflection?

a)

at mid-span

b)

supports

c)

point of loading

d)

throughout

48.

A simply supported beam has equal overhanging lengths and carries equal concentrated loads P at ends. Bending moment over the length between the supports

a)

Is zero

b)

Is a non-zero constant

c)

Varies uniformly from one support to the other

d)

Is maximum at the midpoint

49.

A massless beam has a loading pattern as shown in the figure. The maximum bending moment occurs at

a)

Location B

b)

2675 mm to the right of A

c)

2500 mm to the right of A

d)

3500 mm to the right of A

50.

What will be the variation in the BMD for beam shown in figure. Assume length = 2m

a)

Rectangular

b)

Square

c)

Trazoidal

d)

Triangular

51.

What will be the maximum shear force when the cantilever beam is loaded with UDL throughout?

a)

wl

b)

wl2/2

c)

wl2/4

d)

w

52.

Where do the maximum BM occurs for the beam given the figure?

a)

-54 kNm

b)

-95 kNm

c)

-105 kNm

d)

-65 kNm

53.

What is the SF at support B?

a)

5 kN

b)

3 kN

c)

2 kN

d)

0 kN

54.

The relationship between maximum slope and bending moment is

a)

directionally proportional

b)

inversely proportional

c)

relatively proportional

d)

No relationship between them

55.

A simply supported beam of span as shown in figure is subjected to a concentrated load w at its metre span and also to a uniformly distributed load equality w, what is the total diffraction it its midpoint.

a)

18 WL3 /384 EI

b)

13 WL3/ 384 EI

c)

5 WL3/ 384 EI

d)

8 WL3 /384 EI

56.

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

a)

Increase the area moment of inertia

b)

Increase the span of the beam

c)

Select a different material having lesser modulus of elasticity

d)

Magnitude of the load to be increased

57.

At the fixed end of cantilever beam, deflection is __________ and slope is ___________.

a)

Maximum, Maximum

b)

Zero, Maximum

c)

Maximum, Zero

d)

Zero, Zero

58.

The product of Modulus of Elasticity (E) and Moment of Inertia (I) is called as

a)

Polar moment

b)

Flexural Rigidity

c)

Stiffness

d)

Modulus of rigidity

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