Lab report 1 ( reaction of forces on a simply supported beam) PDF

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It is lab report describing the procedure to analyze reaction of forces on a simply supported beam....

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ENGINEERING DYNAMICS LAB REPORT

SUBJECT: REACTIONS ON A SIMPLY SUPPORTED BEAM SUBMITTED TO: UMAIR ASHRAF KHOKHAR SUBMITTED BY: MUHAMMAD ABUBAKAR SHAHZAD REGD.NO: 2020-ME-121 SECTION: C DEPARTMENT OF MECHANICAL ENGINEERING

1. EXPERIMENT NO. 1: Determining reactions on supply supported beam. 2. OBJECTIVES:  

To determine the Reactions Forces acting on a Simply Supported Beam. To calculate the Mean Percentage Error by comparing the experimental values with the theoretical reaction forces.

3. APPARATUS: • Simply Supported Beam apparatus • Meter Rod • Hanger • Weight Balance • Loads

Figure 1: Beam Apparatus

4. PROCEDURE: a) Take the simply supported beam apparatus and clean it properly.

b) Take two spring balance and attach their one ends to the beam. c)Tie the other ends to the beam support apparatus. d) Measure the total distance L between the two supports. e) Tie three hangers with the beam at some distances L1, L2 and L3 respectively. f) Add weights to the hangers and note the reactions from the two spring balances. g)Repeat the experiment by adding different weights to the hangers. h) Note the reactions for all of them. i) Now, calculate the theoretical reaction forces from the following equations: Ra + Rb = W1 + W2 + W3 & Rb x L = (W1 x L1) + (W2 x L2) + (W3 x L3) From these equations, we can calculate the theoretical values of Ra and Rb. j) After calculating these experimental and theoretical values. k) Determine the percentage errors in these values. l) Find the mean percentage error.

5. OBSERVATIONS: Total Length= 24.1 EXPERIMENT LENGTH(Inches) AL REACTIONS (N)

W1

W2

W3

L1

L2

L3

RA

RB

THEORATIC AL % ERROR REACTION S (N) RA RB %RA %RB

1.25

1.75

0.75

7.4

14.4

20.8

1.5

2

1.67

2.08

2.25

1.75

2.25

5.3

13.1

17.6

3.1

3.5

3.3

2.45

2.25

2.25

3.25

3.5

14.6

20.2

3.5

4.5

3.34

4.41

3.25

2.25

3.25

4.4

12.1

19.2

4.3

4.3

4.44

4.31

2.25

2.25

2.25

3.6

8.8

16.2

4

4

4.08

2.67

LOADS(Lbs.)

MEAN %ERROR IN RA =3.30% MEAN %ERRORIN RB =1.88%

6. THEORY:  BEAMS: “Beams are horizontal structural components used to support lateral loads.” OR

10.4 % 5.94 % 4.9 % 3.1 % 1.96 %

3.7% 1.32% 1.95% 2.6% 6.37%

“A beam is a structural element that primarily resists loads applied laterally to the beam's axis. Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, that in turn induce internal stresses, strains and deflections of the beam. Beams are characterized by their manner of support, profile (shape of cross-section), length, and their material.” Historically beams were squared timbers but are also metal, stone, or combinations of wood and metal such as a flitch beam. Beams can carry vertical gravitational forces but are primarily used to carry horizontal loads (e.g., loads due to an earthquake or wind or in tension to resist rafter thrust as a tie beam or (usually) compression as a collar beam). The loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent structural compression members and eventually to ground. In light frame construction, joists may rest on beams. In carpentry, a beam is called a plate as in a sill plate or wall plate, beam as in a summer beam or dragon beam. Beams are traditionally descriptions of building or civil engineering structural elements, but any structures such as automotive automobile frames, aircraft components, machine frames, and other mechanical or structural systems contain beam structures that are designed to carry lateral loads are analyzed in a similar fashion.

Figure 2: Beam

 ON BASIS OF GEOMETERY: On the basis of geometry, there are following types of beams:

a) Straight beams: Beams with straight profile are called straight beams.

Figure 3: Straight Beam

b) Tapered Beams: Beams with tapered cross section are called tapered beams.

Figure 4: Tapered Beams

c)Curved Beams: Beams with curved profile are called curved beams.

Figure 5: Curved Beams

 On the basis of Equilibrium Positions: On the basis of equilibrium conditions, there are two types of beams:

a)Statically Determinate Beam: Statically determinate beams are those beams whose reactions can be determined using equilibrium conditions.

Figure 6: Statically Determined Beams

b) Statically Indeterminate Beam: Statically indeterminate beams are those beams whose reactions cannot be determined using equilibrium conditions alone.

Figure 7: Statically Indeterminate Beams

 On the basis of Loads: On the basis of geometry, there are following types of beams:

a)Simply Supported Beam A beam supported on the ends which are free to rotate and have no moment resistance is called simply supported beam. OR A simply supported beam is a type of beam that has pinned support at one end and roller support at the other end. Depending on the load applied, it undergoes shearing and bending. It is the one of the simplest structural elements in existence.

Figure 8: Simply Supported Beams

b) Overhanging Beam A simple beam extending beyond its support on one end is called overhanging beam. OR An overhanging beam is a beam that has one or both end portions extending beyond its supports. It may have any number of supports. If viewed in a different perspective, it

appears as if it is having the features of simply supported beam and cantilever beam.

Figure 9: Overhanging Beams

c)Cantilever Beam

A projecting beam fixed only at one end is called cantilever beam. OR A cantilever beam is fixed at one end and free at other end.

Figure 10: Cantilever Beams

d) Continuous Beam: A beam extending over more than two supports is called continuous beam. OR A continuous beam has more than two supports distribute d throughout its length.

Figure 11: Continuous Beams

e)Fixed Beam: A beam supported on both ends and restrained from rotation is called fixed beam. OR As the name suggests, fixed beam is a type of beam whose both ends are fixed.

Figure 12: Fixed Beams

7. Applications: 1. Simply supported beams are easy to design & sometimes overlook critical factors (i.e. indeterminacy) which continuous beam includes. Hence, they allow free expansion, reduced cost, reduced calculations and easy erection procedure. They also reduce redundancy, that makes them practically useful in some structures. 2. The Beam apparatus can be used for an almost limitless number of experiments, such as the determination of the Elastic Modulus for beams of different materials.

3. Most of the bridges we come across in our daily are simply supported. While the beams of regular housing buildings and apartment buildings are not truly simply supported as they have partial fixity. The decks of bridges and precast structures are primarily supported by simply supported beams. 4. Beams are majorly used in house and building to provide support to their structures, floors and roofs to a vertical load bearing structure. 5. Internal supports are provided internally, dividing the full member into parts so the external reaction can be found for each part easily. 6. H Beams (steel) are used for construction of aero planes, trains and ships. 7. Beams are also used in network towers as well as in electricity towers. 8. Beaming structures are also used in wind mills and in large structures like dam turbines....