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Structural Analysis Cardboard project, Assignments of Structural Analysis

Royal Melbourne Institute of Technology (RMIT)Structural Analysis

Assignment Instructions: You are required to design a section of Tunnel beams and calculate the section properties (Centroid, Center of Mass, and Moment of Inertia) and produce a cardboard with the section profile designed. This individualized section will have a relatively large bending stiffness (Second Moment of Inertia)

Typology: Assignments

2022/2023

Uploaded on 04/24/2023

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CARD BOARD PROJECT COVER SHEET
Student name & ID: Christina Maso (S4024052)
Profile shape: Section of Tunnel Beam
From my student number 4024052
Overall outer radius of my cardboard “Rout” cm = 20.2 cm rounded to =20 cm
Overall inner radius of my cardboard “Rin” cm = 14.2 cm rounded to =14 cm
The bw should be Rout/10. = 2cm
See instructions below for “bw” and other dimensions.
My section tunnel beam design
(Software used : SolidWorks)
Instructions:
You are required to design a section of Tunnel beams and calculate the section properties
(Centroid, Center of Mass, and Moment of Inertia) and produce a cardboard with the section
profile designed. This individualized section will have a relatively large bending stiffness
(Second Moment of Inertia). Shown below is a general cross section of a special aluminum
tunnel functioned as a beam.
1. You are required to use the image in Figure 1 (b) with personalized cutting area for
your cardboard project as per the instructions below and further explained by
Sri/Jianhu in the classes or consultation sessions. The shaded area should remain in
your design. The width of cross bars is bw.
2. The personalized cutting areas should be within the grey area and they could be any
combination of the two different shapes from square (a×a), triangle (a×b), circular (a)
and circular segment (a×ϴ). You need to design its sizes and locations to maximize
the cutting area and provide the key dimension such as a, b and ϴ if they are
applicable in your submission.
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Download Structural Analysis Cardboard project and more Assignments Structural Analysis in PDF only on Docsity!

CARD BOARD PROJECT COVER SHEET

Student name & ID: Christina Maso (S4024052)

Profile shape: Section of Tunnel Beam From my student number 4024052 Overall outer radius of my cardboard “Rout” cm = 20.2 cm rounded to =20 cm Overall inner radius of my cardboard “Rin” cm = 14 .2 cm rounded to =14 cm The bw should be Rout/10. = 2cm See instructions below for “bw” and other dimensions. My section tunnel beam design (Software used : SolidWorks)

Instructions:

You are required to design a section of Tunnel beams and calculate the section properties (Centroid, Center of Mass, and Moment of Inertia) and produce a cardboard with the section profile designed. This individualized section will have a relatively large bending stiffness (Second Moment of Inertia). Shown below is a general cross section of a special aluminum tunnel functioned as a beam.

  1. You are required to use the image in Figure 1 (b) with personalized cutting area for your cardboard project as per the instructions below and further explained by Sri/Jianhu in the classes or consultation sessions. The shaded area should remain in your design. The width of cross bars is bw.
  2. The personalized cutting areas should be within the grey area and they could be any combination of the two different shapes from square (a×a), triangle (a×b), circular (a) and circular segment (a×ϴ). You need to design its sizes and locations to maximize the cutting area and provide the key dimension such as a, b and ϴ if they are applicable in your submission.
  1. For student numbers ending with an even number or 0, the overall sizes Rout =16 cm + largest two even number /10 and Rin=14cm+last student number/1 0. e.g., s means 6 and 4 are the two largest even integers, so the width of the cardboard should be Rout =16cm +64/10 = 22.4 cm=22.5 cm and Rin=14cm+0/10=14.0cm, subject to a minimum of 0.5 cm (i.e., if the calculations show less than 5 mm, maintain 5 mm as the minimum difference between the R’s.)
  2. For student numbers ending with an odd number, the overall sizes Rout =16cm + largest two odd number /10 and Rin=14cm+last student number/10.; e.g., s means 9 and 7 are the two largest odd integers, so the width of the cardboard should be Rout =16cm +97/10 = 25.7 cm=25.5cm. Rin=14cm+7/10=14.7cm=14.5cm, subject to a minimum of 0.5 cm (i.e., if the calculations show less than 5 mm, maintain 5 mm as the minimum difference between the R’s.)
  3. The bw should be Rout/10. For the given example in 4. bw=2.55cm =2.5cm. (5mm is minimum difference).
  4. These dimensions may be slightly adjusted subject to our permission.
  5. On the back side of the image, breakdown the complex shape into simple regular areas such as square, rectangles, triangles, circle and circular segment etc.
  6. Use the coordinate system marked in Figure 1(b) to do your calculations.
  7. Calculate: (1) Centroid (𝑥̅, 𝑦) with O as origin, (2) Center of Gravity (or Mass) with O as origin, (3) Second moment of inertia (𝐼 (^) ̅and 𝐼 ) with centroid as origin, and (4) Radius of gyration with centroid as origin.
  8. For centre of gravity or mass, consider all sections as aluminum material.
  9. To prove the moment of inertia is relatively large. Please compare it to a section design with lower value.
  10. Submit THIS cover sheet and the calculations by the due date noted on Canvas.
  11. Any questions email Sri / Jianhu. Figure 2 provides some examples of acceptable profile shape without individualized dimensions. Figure 2. Acceptable profile shapes without dimensions

Calculations:

The complex shape was broken down into simple regular areas. Shape 1: the outer circle with R= 20cm Shape 2 and 2’ right triangles are congruent figures; therefore, all dimensions and area are the same. Shape 3 and 3’ are also congruent figures and all dimensions and area are the same. Dimensions:

Centroid:

 - 1 0 1256.64 elements ỹ A ỹ.A - 2 7.5 - 84.5 - 633. - 3 5.45 - 79.21 - 431.
  • 2' - 7.5 - 84.5 633.
  • 3' - 5.45 - 79.21 431.
  • ȳ = - 1 0 1256.64 elements x᷉ A x᷉.A - 2 - 7.5 - 84.5 633. - 3 5.45 - 79.21 - 431.
    • 2' 7.5 - 84.5 - 633.
    • 3' - 5.45 - 79.21 431. - x̄=

Second Moment of inertia:

Ix: