TITLE : CANTILEVER BEAM

What is cantilever beam?

A cantilever beam is a beam that is only supported on one of its ends.

The beam bears a specific weight on its open end as a result of the support on its

enclosed end, in addition to its structural integrity. Cantilever construction is

popular in many kinds of architectural design and in other kinds of engineering,

where professionals use terms like end load, intermediate load, and end moment

to identify how much a cantilever beam will hold. The term moment is related to

torque and to a theoretical load on a beam.

In residential architecture, cantilever design is often used for creating balconies

and other extensions above ground level. Famous architects like Frank Lloyd

Wright were known to take advantage of cantilever beam construction to

provide for parts of a building that protrude from a supported section. The use

of cantilever beam setups and similar cantileverengineering is also often seen in

bridges and similar projects. Carpenters might think ofcantilever beam design in

terms of wooden beams, but in other kinds of projects a cantileverdesign is

applied to a concrete slab or a metal girder.

A specific use of cantilever beam construction is often part of a temporary

construction project. While a bridge or other project is in

transition, cantilever design provides for structural integrity while only one side

of a beam is supported. Later, that beam may be supported on both sides.

Engineers can show diagrams of how cantilever design will help ensure stability

mid-way through a building project as part of a safety study.

Architects and engineers also use cantilever beam structures for the overhangs

that are often a part of various buildings. Airports, university campuses, office

complexes, and other areas will often include exterior structures that

use cantilever beam construction for different intentions in building design.

These overhanging elements can provide shelter from the elements or a

decorative aspect to a building. In some cases, an "open style" cantileverdesign

fits into a modern or artistic design for a space, where planners have blended

practicality with aesthetic appeal.

Those who are interested in observing how cantilever design is used in modern

engineering can easily find many visible instances of this engineering method at

work in their local communities. A detailed study of this kind of design can

better prepare a student for entrance into an engineering or architectural

program. It can also increase a student's understanding of how professionals

implement this kind of design to both residential and commercial projects.

Theory

For this experiment, the flexural strain induced by a loading force on a cantileverbeam will be used to determine the flexural stress of the beam. By Hooke’s Law, thestress acting in the beam is equal to the beam material’s modulus of elasticity, E.

Second Moment Area

The second moment area, including the area moment of inertia, also known as moment of inertia of plane area, or second area moment, is a property of a cross section that can be used to predict the resistance of beams to bending and deflection, around an axis that lies in the cross-sectional plane. The deflection of a beam under load depends not only on the load, but also on the geometry of the beam's cross-section. This is why beams with higher area moments of inertia, such as I-beams (properly denoted as: wide-flange beams), are so often seen in building construction as opposed to other beams with the same cross sectional area.

The area moment of inertia involves angular kinetic energy or momentum. Often, each of these may simply be referred to as "moment of inertia," but it is suggested to distinguish the symbols, I for the mass ones and J for the area ones. Which inertia is meant (bending, twisting, or kinetic) is also usually clear from the context, if not from the units: both moments of area have units of length to the fourth power [m4] (distinguished only by whether a beam is being bent or torqued), where as the kinetic mass moment of inertia has units of mass times length squared [kg*m2].

I y=bh3

12=20 × 63

12=360 mm4

EXPERIMENT :

Bending In The   Cantilever Beam

OBJECTIVES:

To compare the analytical and experimental values of the stress inthe stress in cantilever beam.

To present the results in terms of statistical values.

To become acquainted with various items of structural testingequipment.

compare the effects of the bending moment on the cantilever beams of different modulus of elasticity

comparing the modulus of elasticity values obtained from the experiment with the value assumed in the calculation of E

EQUIPMENT

Structural testing frame.

Alloy, Brass, & Aluminium bar 6 x 20 x 1000mm

3 weight 5 N.

Calibrated weights.

Measuring instruments as required.

PROCEDURE

choose bar set at labsheet.

measure the cross section at the bar

tie bar on the bond on a frame

tie the dial gauge on the frame with thedial gauge is adjusted to zero when the bar is not charged

put the burden on the desired place as scheduled

repeat steps 2 to 7 for other bar

Modulus of Elasticity for 3 Material

No Material Cross Section E

1 Alloy 20 ×6 mm2 210000 N /mm2

2 Brass 20 ×6 mm2 105000 N /mm2

3 Aluminium 20 ×6 mm2 69000 N /mm2

Second Moment Area :

I y=bh3

12=20 × 63

12=360 mm4

Force = 17.5 N

Calculation shift  f :

f = F L3

3EI y

Where,F = Force (N)E = Modulus of Elasticity (N/mm2¿

Iy = Second Momen Area (mm4)L = Length of Beam (mm)

Calculation f for Alloy :

1).

f = F L3

3 EI y

f =17.5(300)3

3 (210000 )(360)

f =472.5 ×106

226.8 ×106

f =2.08mm

2).

Length, L : 300mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 210000N/mm2

Length, L : 400mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 210000N/mm2

f = F L3

3 EI y

f =17.5(4 00)3

3 (210000 )(360)

f = 1.12× 109

226.8 ×106

f =4.94 mm

3).

Length, L : 500mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 210000N/mm2

f = F L3

3 EI y

f =17.5(500)3

3 (210000 )(360)

f =2.1875 ×109

226.8 ×106

f =9.65 mm

Calculation f for Brass :

1). Length, L : 300mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 105000N/mm2

f = F L3

3 EI y

f =17.5(300)3

3 (105000 )(360)

f =472.5 ×106

113.4 ×106

f =4.17 mm

2).

Length, L : 400mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 105000N/mm2

f = F L3

3 EI y

f =17.5(4 00)3

3 (105000 )(360)

f = 1.12× 109

113.4× 106

f =9.88mm

3).

Length, L : 500mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 105000N/mm2

f = F L3

3 EI y

f =17.5(5 00)3

3 (105000 )(360)

f =2.188 ×109

113.4× 106

f =19.29 mm

Calculation f for Aluminium :

1). Length, L : 300mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 69000N/mm2

f = F L3

3 EI y

f =17.5(300)3

3 (69000 )(360)

f =472.5 ×106

74.52 ×106

f =6.34 mm

2). Length, L : 400mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 69000N/mm2

f = F L3

3 EI y

f =17.5(4 00)3

3 (69000 )(360)

f = 1.12× 109

74.52× 106

f =15.03mm

3). Length, L : 500mm

Second Moment Area, Iy: 360mm4

Force, F : 17.5N

Modulus of Elasticity, E : 69000N/mm2

f = F L3

3 EI y

f =17.5(5 00)3

3 (69000 )(360)

f =2.1875 ×109

74.52× 106

f =29.35 mm