KAA 110 - Engineering StaticsLab Task 3: Reactions, Internal Forces and Moments of BeamsReport due...

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KAA 110 - Engineering StaticsLab Task 3: Reactions, Internal Forces and Moments of BeamsReport due date: Two (2) weeks from date of lab session  Objective  To observe the behavior of a beam subject to external forces To predict the reactions of the beam under different load cases To evaluate these predictions by comparing with measured values To use effective engineering communication by clearly and concisely expressingtechnical informationEquipment  Scales Supports A 4m plank Tape measureExperimental Procedure (1) Zero each scale (with all loads being removed from the scales)(2) Weigh two team members (P1 and P2), and record the body weights.Record all loads, load positions and reactions for the following load cases: (3) Load Case 1: Measure the beam self weight by resting two ends of the beam on twosupports over the scales (the summary of the readings from the scales is the weight ofthe beam and the supports).(4) Load Case 2: Have team member one (P1) load the beam at the ¼ point.(5) Load Case 3: Have team member one (P1) load the beam at the ¼ point and the secondteam member (P2) load the beam at the ¾ point.(6) Load Case 4: If only one person (P1) is loading the beam, determine the location of P1 tomake the reaction R1 = 40kg.(7) Load Case 5: Reaange one support so that it is beneath the 3/5 point of the beam.Have one team member (P1) at the 1/2 point of the beam and determine the location ofa second team member (P2) on the cantilever portion so that the reaction at the otheend of the beam is just zero.Analysis For load case 1:  Make a good sketch of the apparatus, ensuring that you define a coordinate system, alldimensions and all forces. From the reaction forces, estimate the weight of the beam and supports and suggestwhere it could be assumed to act.For load cases 2 - 5:  Make a good sketch of the apparatus, ensuring that you define a coordinate system, alldimensions and all forces. From the known loads, predict the two reactions. Compare the predicted and measured reactions. Please draw shear force and bending moment diagrams of each load case, consider theeam self-weight as a UDL.Report Refer to the Ruic (for Lab 3). One individual lab report is required per student; group reports are not permitted. Electronic submission via Mylo only by the due date. Pdf or Doc format only.Please ensure the following:  Follow the supplied ruic when preparing your reports – this will help you maximizeyour marks. The report needs to be well organised and well structured, including headings, sketches,figures and tables as appropriate. KAA 110 - Engineering Statics Marking RuicLab 3: Reactions, Internal Forces and MomentsStudent Name: ________________________________________ Student Number:_________________________________________ Criteria 80-100% 65-80% 50-65% 0-50%1. Apply standardtest procedures,60%Accurately calculate the predicted esults based on the selected coordinate system and equiliium equations. Clearly interpret the measured esults  Accurately calculate the differences etween the predicted and measured values and clearly present your comparison in a table Calculate the predicted results ased on the selected coordinate system and equiliium equations. Interpret the measured results Calculate the differences between the predicted and measured values Eor in predicted or measured esults but not both Some insight into measured results given Unexpectedly large  eors identified Eor in predicted and measured esults or results missing Little insight given into measured esults 2. Present reportin a professionalmanner,40%Coectly list any assumptions and factors that may contribute to differences between predicted and measured values Test apparatus clearly sketched and other diagrams to appropriate scale, all well labelled Concisely discuss observations Coectly use language without spelling and grammar eors List most important assumptions and factors which contribute to differences between predicted and measured values Provide a sketch of the test apparatus and some additional diagrams, all well labelled Observations discussed with most important points covered Minimal spelling and grammar eors Important assumptions not listed or some incoect assumptions listed A sketch is provided, but information is missing or the sketch is poorly presented Some meaningful observations made Written work can be understood but has spelling eors or poor grammar Incoect assumptions listed or assumptions not listed Sketch not presented or of not legible Observations not discussed Sections of written work cannot be understood.

Dr Shweta · Accepted Answer

Lab: Reactions, Internal Forces and Moments of Beams
These experiments help us to find the different internal forces, reactions and moments of forces on beams when subjected under different conditions. A beam is a structural element that can resists the loads which are applied laterally on its axis. Whenever a beam is subjected to any external force then three internal forces developed in the beam – the normal force (N), the shear fore(V) and the bending moment(M). These forces can be explained as below:  
a) The Shear force (V) is equal to the algebraic sum of all vertical forces present on the beam either on the left-hand side or the right-hand side.
b) The bending moment(M) is equal to the algebraic sum of the moments of all the forces present on the beam either on the left-hand side or the right-hand side.
c) The normal force (N) is the force exerted by the surface on the body. When a body is at rest then the downward force is the weight (W) which is balanced by the upward weight or normal force (N) and thus the net force acts on the body equals to zero.
These internal forces can be calculated using following steps: 
· Step 1: Draw a free body diagram (FBD) of the given set-up
· Step 2: Find the reactions at the external supports
· Step 3: Put loads at their specified locations
· Step 4: Then find the different forces- N, V, M at equilibrium
Before starting the experimental procedure all the scale were initially set at zero by removing all the loads from the scale.
 Then, the weight of two team members (P1 and P2) were measured and the recorded body weights are: 
Weight of P1 is 67 Kg and weight of P2 is 62.3 Kg
In this lab work we have assessed the different types of internal forces that acts on the beam whenever it is subject to an external load. Internal forces are generated by the objects of the system which in turn causes acceleration in different parts of the system but cannot cause any acceleration in the center of mass. The five fundamental changes that can occur in the beam due to the application of external load are – the compression, tension, shear, bending and torsion.  So, if we applied load properly over the beam at a suitable position then there will be no change in the internal system of beam and thus the chances of bending of beam will be minimum or less likely. This is termed as the position of equilibrium where the combination or summation of all the external forces applied on the system becomes equals to zero and therefore, we can say that internal forces are acting in different directions and maintains the equilibrium. 
Then the different cases are solved as shown below: 
1. Load Case 1: The beam self-weight is measured by resting the two ends of the beam on two supports over the scales. This is a simply supported beam, here the end supports exerts only the forces upon the bar not the moments as shown below: 
Beam
Weighing balance
A. The good sketch of the apparatus defining all coordinate system, all dimensions and all forces is shown as below: Y-axis
 Net R = upward
Z-axis
R2 Acts upward
R1 Acts upward
X-axis
MB = wL2/12  
MA = wL2/12 
W2 = 9.9 Kg
Acts downward
   Net W = downward
w1 = 9.9 Kg
Acts downward
                  Here, R1 = W1, R2 = W2 and Net R = Net W
The X axis, Y-axis and Z-axis are the three coordinates here and here the weight is acting in the -Y axis while the reaction or normal force is acting in the +y -axis. If we check the components of reaction force then RcosƟ will act in the X-axis and RsinƟ will act in the Y-axis.
That is the total load exerted by the beam's self-weight is completely balanced by the sum of the two reaction forces at the two supports.
Therefore, the beam is at equilibrium with net force equals to zero and no turning effect is there i.e., both MA and MB cancel each other as both are equal in magnitude and opposite in direction. 
B.  From the reaction forces, the weight of the beam is estimated as: 
For a simple supported beam, 
R1 *L/2 = W1* L/2 and R2 *L/2 = W2* L/2  
Net R = R1 + R2 
So, Net R = 9.9 + 9.9 = 19 N
And since the beam is in equilibrium with no turning so net weight of the beam is equal to 
19 N as the total load exerted by the beam's own weight is completely balanced by the sum of the two reactions at the two supporting ends.
C. The weight of the beam will act in downward direction to maintain the beam at equilibrium position.
2. Load Case 2:

work for whole report. I need to get 65-80% mark

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