Structures Standing Still : Project final submission
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The document details a final project by Dr. Dan Dickrell on the statics of everyday objects, focusing on the design and cost analysis of a truss structure. It includes calculations for load, stress, and buckling analysis of various members, concluding that certain members will fail under specified conditions. The total cost of the truss design is calculated to be $1,507, and the analysis notes the safety of the design regarding compressive and tensile forces.
Structures Standing Still : Project final submission
- 1. Structure Standing Still: The Statics of EverydayThe Statics of Everyday Objects by Dr. Dan Dickrell Project Final SubmissionProject Final Submission
- 2. Design Scratch: My truss design (drawing by AutoCAD) labeling the joint locations withMy truss design (drawing by AutoCAD) labeling the joint locations with letters, and showing important dimensions locating the joints within the design.
- 3. Cost Analysis:y My design labeling the joint locations showing important dimensions locating the joints within the design.
- 4. Cost Calculation: Given free pin joint at B & two free reaction points, a pinp j p , p joint at A and a roller at C. AB=BC=DE=4 m Cost= 3*(75+4^4) = $993 AD=BD=BE=CE=2.31 m Cost 4*(75+2 31^4) $414Cost= 4*(75+2.31^4) = $414 Total member cost= $1407 Joint (A B C) = $0 (Free)Joint (A, B, C) $0 (Free) Pin joint (D, E) = $50 Total pin joint cost =$50*2= $100p j Total truss (bridge) cost= 1407+100= $1507
- 5. Load Calculation: Blue member (AD, DE, CE) =Compression buckling Red member (AB, BC, BD, BE) = Tensile yielding Forces in members: AB=BC=DE=8 66 KNAB=BC=DE=8.66 KN AD=BD=BE=CE= 10 KN Force Type: AB 8 66 KN (T il i ldi )AB=8.66 KN= (Tensile yielding) BC=8.66 KN= (Tensile yielding) DE=8.66 KN= (Compression buckling) AD=10 KN= (Compression buckling) BD=10 KN= (Tensile yielding) BE=10 KN= (Tensile yielding)BE 10 KN (Tensile yielding) CE= 10 KN= (Compression buckling)
- 6. Stress Analysis: Material Selection: Truss Material: Aluminum Shape: Hollow Pipe Yield strength: 95 MPa = 95000 KN/m² Factor of safety=3 (Assumed) Equation: Yield strength or stress = Load* Factor of safety / Sectional Area After calculation on tensile members: For BD=BE= 10 KN; Outer diameter= 50 mm Inner diameter= 45.8 mm For AB=BC=8.66 KN; Outer diameter= 50 mm Inner diameter= 46.4 mm
- 7. Buckling Analysis:g y Euler’s Equation: F i iti l fF= maximum or critical force E= modulus of elasticity=95 Gpa I= area moment of inertia= ∏/2*(R^4-r^4) L= unsupported length of column, K= column effective length factor, For both ends pinned= 1.0. For AD, CE member: Outer diameter( R )= 50 mm & Inner diameter (r)= 48 mm & L= 2.31 m (proposed di i )dimension) Applying Euler’s equation, Maximum or critical force, F= 1.18E+7 GN So our designed load 10 KN in AD & CE member is safe from compressive buckling. F DE bFor DE member: Outer diameter( R )= 50 mm & Inner diameter (r)= 48 mm & L= 4 m (proposed dimension) Applying Euler’s equation Maximum or critical force F 3 93E+6 GNApplying Euler s equation, Maximum or critical force, F= 3.93E+6 GN So our designed load 8.66 KN in DE member is safe from compressive buckling.
- 8. Final Remarks: AD & CE will fail first due to Compression buckling &buckling & BD & BE will fail first due to tensile i ldiyielding. Important Notes: I have ignored some parameters such as weight of members, d namic loads ind loaddynamic loads, wind load.
- 9. Thanks