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Unformatted text preview: Karthik Ramani School of Mechanical Engineering How to fulfill a certain type of function and with what type of a function carrier? Neither desirable nor possible to implement in every technical solution. Represent strategies that are applicable under certain conditions. Designers must strike a balance between competing demands. ! ! " $ ! # $ ! % $ ! & !% ' !& !' ! ! $ !" ! " ! # ! % !" & () , -+ *+ Identify the ideal shape for loaded parts, regardless of material. This goal is met when all the material is stressed equally.
Uniform stress through the part. Minimum weight (stress close to strength). Form ~ constraints that define the envelope Form = evolution of components + relative configuration + how they are connected to each other
Where are the loads applied?
Location and direction * Where is the part restrained?
Location and direction Therefore where should the material be placed, and where should it be removed? Magnitude of the loads are not important yet and strength of the material is not important yet. We seek the optimum shape regardless of the magnitude of the loads and strength of material. )
Strong stress patterns:
Tension/compression. Bending of i-beams. Torsion of hollow bars. Transverse shear. ( )
Weak stress patterns:
Bending of non-i-beams. Torsion of solid sections. Spot contact. ( Design the shape so that applied loads induce strong stress patterns in the members. ( + + *+ - If a force or a moment is to be transmitted from one place to another with the minimum possible deformation, then the shortest and most direct force transmission path is the best This principle which leads to minimum number of loaded areas ensures:
Minimum use of materials (volume and weight), and Minimum deformation. " (
Triangle Tetrahedron Force flow + + *+ - Leverage
I-Beam Torsion of hollow tube # *(
Identify location of loads Identify direction of loads Put material in direct path of loads Triangle: For planar force transmission from point to line Tetrahedron: For spatial force transmission from point to plane. % Triangle Principle & Leverage Principle (a) No leverage (b) Too little © Too much (d) near optimal ' * -/ ( *+ Visualize force flow as fluid flow Fill in material where fluid flows Remove material where it does not Rounded fillets – blended surfaces 0, ( *+ - Material should leverage on the loads. I-Beam principle:
For bending place material far from the neutral axis Remove material near the neutral axis: where stress = 0 Torsion principle: (circular cross section)
Use a hollow tube, not a solid one Force Flow Principle Force Flow Principle Good shapes for bending moment (a) when the axis of the moment is known (b) when the axis of moment is not known. Force Flow Principle
Leverage principle for torsion: (a) Not enough leverage, (b) too much leverage, (c) Near-optimal. Connecting Rod " Reducing Stress Concentration (a) Severe stress concentration (b) use large radius if possible (c) Add groove if large radius is not possible (d) undercut shoulder helps If (b) or (c) cannot be used (e) short step.
# Force Flow Stiffness Interactions
Redundant load paths can lead to undesirable interactions because load divides in proportion to stiffness of load paths % Strength-stiffness relationship
• The triangular addition could actually weaken the part. • Design redundant load carrying members so that the strength of each member is approximately proportional to its stiffness. & Residual Stresses in Assemblies In built-up structures having redundant load paths, the undesirable effects of manufacturing process induced residual stress can be reduced by making one load path relatively stiff compared to all others. ' Stiffness Mismatch: Stress Concentrations
• Occurs when load transfer deformation between components is not matched. • Design related components in such a way that, under load, they will deform in the same sense and if possible, by the same amount. Force Flow Interruptions " Violation of Direct Path " (
Buckling: What and why? Why do things buckle? ) +1- Strong stress pattern (compressive stresses) Small deflection – imperfection Weak stress pattern (bending) Unstable - failure " Bucking! " Local Buckling (a) Torsion (b) Compression in an I-Beam "" 23 *
Identify compressive loads Identify potential failure deflection Use stiffeners to prevent initial deflection Reduce chances of buckling ( *+ - "# 1
Limited space Cost Manufacturing process Function Aesthetics Use of different materials ,- "% Part Synthesis Critique
Part shown is to transmit torque, tension, compression from one end to the other through the holes shown. Redesign the shape of this part to make it as efficient as possible. Consider the constraints imposed by manufacturing. "& "' " # # # Part Synthesis Exercise # ( ) $* #" ## #% #& #' # % % % % %" %# %% %& %' % ...
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This note was uploaded on 07/09/2010 for the course ME ME553 taught by Professor Ramahni during the Spring '09 term at Purdue University Calumet.
- Spring '09
- Mechanical Engineering