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Structures 1
Fichas del conjunto (26)
- 14 key concepts• Equilibrium- a requirement that all forces and moments balance
• Compatibility- a requirement that all displacements are consistent throughout structure
• Constitutive law- relationship between forces/ stresses and displacements/ strains
• Failure model- mathematical description of when structure no longer performs its designed function - 2TractionStress vector
lim (? ➡ 0) ?P/ ?A = dP/ dA = t (traction) - 3How many unique stress tensor elements?6
- 4Complementary shearτₓᵧ = τᵧₓ (Same for other shear components) because of rotational equilibrium
- 5Centroid∫y dA = 0 (line along which force must be applied for equilibrium in long, thin rod)
- 6What is failure?When a structure reaches a condition at which it no longer carries out the task it was originally designed to do (doesn't necessarily mean breaking)
- 7Constitutive relationship for 1-D structureεₓₓ = 1/E σₓₓ + α₁ ΔT
- 8Constitutive relation for plane stress/ membrane structure (2-D)εₓₓ = σₓₓ/E - v/E σᵧᵧ
εᵧᵧ = σᵧᵧ/E - v/E σₓₓ
γₓᵧ = τₓᵧ/ G - 9Pin-jointA component that joins the ends of two rods, constraining their translations to be equal but allowing relative motion
- 10Zero moment conditionNo moment at a pin- joint since it's free to rotate
- 11Typical elastic limit for most materials0.2% strain
- 12Methods of sectionsFocusing on one region of interest, one part of the structure, bypassing other regions
- 13Mechanism vs. structureMechanism defined as a system that can undergo large geometry changes without addition of strain
Structure may only experience a shape change if strain is present (a structure maintains its shape under applied load whereas a mechanism does not) - 14Over-determined frameworkMore solutions (equilibrium equations) than unknowns
- 15Statically determinate systemNo. of unknowns = equilibrium equations (can work out all unknown just from equilibrium equations)
- 16Statically indeterminate systemNo. of unknowns > no. of equilibrium equations (if one of the members of the framework is taken out, could become a structure)
- 17Maxwell's equationM = b + r -2j
M = mobility
b = no. of bars
r = no. of reaction forces
j = no. of pin-joints
(no. of unknowns in a pin-jointed framework = b + r)
(no. of equilibrium equations = 2j) - 18From Maxwell's equation, when M < 0Too many equilibrium equations, infinitely many solutions --> mechanism
- 19From Maxwell's equation, when M = 0Possibly statically determinate unless...
• a mechanism and a redundancy are both present
• infinitesimal mechanism exists - 20From Maxwell's equation, when M > 0Statically indeterminate (or redundant)
- 21Principle of superpositionSum of responses of same structure subjected to different loading conditions is same as if structure were subjected to all load conditions simultaneously
- 22Prismatic beamsBeam with a uniform cross-section throughout
- 23What is defined as a beam?A very long member with length significantly larger than height (at least around 10:1) that primarily resists transverse loads and primarily deflects by bending
- 24Distributed forceForce acting over a part (an area) of the beam- can be constant or linear
Constant force F = w(x) = w at any point x
Linear force F = x(x) = w x/ L at any point x (where w is max force) - 25Point loadConcentrated force at a single point
- 26—
Información
- Descripción
- Undergraduate Structures Fichas sobre Structures 1, creado por Paris Hart el 20/01/2021.
- Creado por
- Paris Hart
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