15 Oct In this project, you are tasked to design a truss beam for an industrial building. The truss beam and the loading are shown. The project has three parts described below. Appropriate
In this project, you are tasked to design a truss beam for an industrial building. The truss beam and the loading are shown.
The project has three parts described below. Appropriate documents are to be submitted at the end of each phase in the format specified by the instructor. re
Part 1 Due date: last day of week 3
Consider the truss beam shown:
a. Draw the Free-Body Diagram (FBD)
b. Solve for the reaction of supports
MET211: Statics
Project
1. Write only on one side of the paper
2. Use consistent units
3. Round off final answers to proper degree of precision or accuracy
4. Underline your final answer
Industrial Roof Truss System Design
An example of an industrial roof truss system
Introduction
In this project, you are tasked to design a truss beam for an industrial building. The truss beam and the loading are shown.
The project has three parts described below. Appropriate documents are to be submitted at the end of each phase in the format specified by the instructor. re
Part 1 Due date: last day of week 3
Consider the truss beam shown:
a. Draw the Free-Body Diagram (FBD)
b. Solve for the reaction of supports
Page 3
image1.png
image2.png
,
MET211 Statics
Structures & Members
Introduction
A two-force member has forces acting on each end. These forces line up with the member and cause either tension or compression.
A truss is formed if several two-force members are joined in one or more connected triangles. Each of the members is pinned at each end and, if carrying a load, is in either tension or compression.
The direction of the member indicates the direction of the tensile or compressive force in the member acting on the joint or pin. The ends of the members are pinned together to form a joint. A member in tension and pinned at a certain joint exerts a pull on the pin.
Each truss member is a two-force member if we neglect the weight of the member. This is a relatively safe assumption since the member weight is often small compared to the loads carried by the truss.
Method of Joints
The method of joints consists of a number of free-body diagrams of adjacent joints.
The first joint selected must have only two unknown forces and one or more known forces.
The unknown forces are determined by using ΣFx = 0 and ΣFy = 0. These newly found forces are used in the free-body diagram of an adjacent joint.
The load in each truss member is found by taking consecutive free-body diagrams of joints throughout the complete truss.
Method of Joints
Example:
Determine the load in each member of the truss shown
Solution:
Step 1. Solve for the external reactions RA and RH.
Step 2. Choose a pin or joint for the first free-body diagram.
Step 3. Draw a free-body diagram of A.
Step 4. Solve for AB
Step 5. Solve for AC
Step 6. Follow the value of a new known load, AB = 6.25, from pin A to an adjacent pin, B.
Step 7. Solve for BD
Step 8. Solve for BC
And so on…
Method of Joints
Step 1.
Solve for the external reactions RA and RH. The first step of the solution is one with which you are already familiar: Solve for the external reactions at points A and H. Taking moments about point H and solving for RA, we obtain:
Method of Joints
Step 1.
Solve for the external reactions RA and RH. The first step of the solution is one with which you are already familiar: Solve for the external reactions at points A and H. Taking moments about point H and solving for RA, we obtain:
Method of Joints
Step 2. Choose a pin or joint for the first free-body diagram.
Note that only four joints—A, D, G, and H—have known forces.
Joint D has four unknowns,
G has three unknowns,
Joints A and H each have two unknowns.
Thus, the first free-body diagram could be of joint A or H.
Let us arbitrarily choose joint A.
Assume member AB to be in compression and member AC to be in tension
Step 3. Draw a free-body diagram of A
Method of Joints
Step 4. Solve for AB
Step 5. Solve for AC
The compression or tension of a member should be indicated following the value with C or T, respectively
Method of Joints
Step 6. Follow the value of a new known load, AB = 6.25, from pin A to an adjacent pin, B.
Step 7. Solve for BD
Step 8. Solve for BC
Method of Joints
Step 9. Knowing the value of BC = 5, move from pin B to pin C and draw a free-body diagram
Step 10. Solve for CD
Step 11. Solve for CE
Method of Joints
Step 12. Reduce your possibility of error.
Go to joint H and work back toward the center of the truss
Step 13. Show RH = 7 kips on a free-body diagram of H
Step 14. Solve for GH, using ΣFy = 0
Step 15. Solve for EH, using ΣFx =0
Method of Joints
Step 16. Knowing GH = 8.75 kips C, move from pin H to a free-body diagram of G
Step 17. Solve for EG, using ΣFy = 0
Step 18. Solve for DG, using ΣFx = 0
Method of Joints
Step 19. Draw a free-body diagram of E showing CE = 7.5 kips, EG = 3 kips, and EH = 5.25 kips .
Step 20. Solve for DE, using ΣFy = 0
Step 21. Check accuracy of calculations, using ΣFx = 0
Method of Joints
Step 22. Label forces for all truss members
Method of Sections
The method of sections is used to solve for the force in a member near the middle of a truss.
The time-consuming method of joints is avoided.
The method of sections consists of cutting a truss into two sections by cutting through the truss where a member force is required; one section is discarded.
A free-body diagram of the remaining section is drawn. On this free-body diagram, we show a tensile or compressive force where each member was cut.
These are equivalent forces that have the same effect as the discarded section had. Suppose that a truss member, cut in two by the method of sections, had been in compression. The free-body diagram would show a force pushing on the remaining half of the member.
Only three members are usually cut at one time, although a partial solution is possible when four or more members are cut.
Method of Sections
Solve for the load in members CB, AB, and JK of the truss shown
Method of Sections
Solve for the load in members CB, AB, and JK of the truss shown
ΣFy = 0
ΣMC = 0
Method of Sections
Solve for the load in members CB, AB, and JK of the truss shown
ΣMD = 0
Method of Members
In the previous truss problems, the truss members were two-force members; there was a force acting at each end of the member; each member was in either tension or compression. The force of a member on a joint had the same direction as the slope of the member. For this reason, we could draw free-body diagrams of individual joints.
Free-body diagrams of joints cannot be used when the members have three or more forces acting on them. A three-force member may be subject to bending, and the force that it exerts on a joint no longer has the same slope or direction as the member.
Therefore, a free-body diagram is drawn of the member, not of the joint.
A frame consists of a number of members fastened together so that each member has two or more forces acting on it. Determining these forces consists of drawing free-body diagrams of individual members or of the complete frame.
Method of Members
Example
Note that the internal forces at B are in opposite directions in the two diagrams. If AB pushes down on CD, then CD pushes up on A
Method of Members
ΣMA = 0
ΣMD = 0
N
References
All figures and examples are taken from
APPLIED MECHANICS FOR ENGINEERING TECHNOLOGY, EIGHTH EDITION, Keith M. Walker, ISBN 978-0-13-172151-7
image2.png
image3.png
image4.png
image5.png
image6.png
image7.png
image8.png
image9.png
image10.png
image11.png
image12.png
image13.png
image14.png
image15.png
image16.png
image17.png
image18.png
image19.png
image20.png
image21.png
image22.png
image23.png
image24.png
image25.png
image26.png
image27.png
image28.png
image29.png
image30.png
image31.png
image32.png
image33.png
image34.png
image35.png
Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.