Structural Integrity Analysis and Sustainability

Assume:

• defined yield point
• no increase in stress after the yield point (no work hardening)
• yield stress is the same in tension and compression
• strain is proportional to the distance from the neutral axis
  • stress is constant
• at the plastic hinge, the moment of resistance remains constant until collapse

Plastic Limit Analysis

• As the bending moment increases, plasticity develops
• The deformed region will start to move in towards the neutral axis
• With increased bending moment the section becomes fully plastic 
• Shape factor: the ratio between fully plastic bending moment and the bending moment at first yield; depends on the shape of the section
• the allowable load increases as the plastic deformation increases, however, there is no further safety (dangerous)

Unsymmetrical section: The neutral axis shifts to  maintain equilibrium

• Can calculate distance,h, by considering the equilibrium
• The resisting moment can also be calculated by taking the moments about the neutral axis
• Fully plastic: neutral axis divides the cross-section into 2 halves with equal area [stress is the same]

Collapse loads: Limit analysis

• plastic hinge develops when a plastic bending moment occurs at a point
• Cantilever beam: only 1 hinge causes collapse; others may require more 
• moment of resistance at plastic hinge remains constant until collapse
• Energy methods: equating work done by the load to the internal work done o moving plastic hinge

Portal frames

• if freely hinged then there is no restraining moment on them
• The possible mode of collapse is one with the smallest load to cause it

Residual stress: removing The bending moment is equivalent to superimposing a moment of opposite sign

Energy Methods

• Strain energy: work done on bar is the average force times the distanced moved
• Torsion: strain energy = work done in twisting

Virtual work

• an alternative way of expressing the equilibrium conditions
• forces are assumed to be constant during displacement
• The total resolved force should be zero at equilibrium
• virtual displacement: any small displacement which is possibly subject to constraints on a body
• Total work of all external forces is zero 

Maxwell Reciprocal Theorem: Deflection at P1 due to force at P2 is equal to the deflection at P2 due to the force at P1

The theorem of least work: equilibrium is the minimum energy state, use to assess the stability of systems

Castiglianos theorem

• displacement: partial derivative of the total energy with respect to force
• fictitious load (Q) introduced to obtain deflection where (point) no load is applied

Shock loading

• Determine energy to be absorbed 
• consider maximum deformation of the system 
• equate to get the distortion or maximum force 

Circular economy: minimal resource loss/waste; minimal responsible virgin resource inputs

Life Cycle thinking and assessment: wider consequences of strategies aimed at making improvements

• The scale of environmental and resource impacts of an activity or function; 'end' use impacts
• Method: goals, data collection, modelling run analysis, check and revise, impact assessment, interpretation
• Impact assessment: assess the impact on Earth of raw materials
• LCA has a role in understanding the benefits of a circular economy
• LCA results can be counter-intuitive
  • e.g. making steel from scrap iron
  • it costs the same amount of energy to use end-of-use recycled energy to use end-of-life recycled scrap as it does to use source scrap as it does to source scrap from recycled sources
• Important to consider the use of sustainable alternatives

Sustainability: quality of life, meeting needs of today without compromising tomorrow

• The environmental, social, and economic performance of a material is crucial for making sustainable decisions
• LCA: identify and develop holistic and robust solutions
• Externalities: external payments such as a tax on businesses for CO2 emissions
• Supplier responsibility: social value in the supply chain (e.g. child/slave labour, conflict minerals, Toxicology)
• Product performance: social value to supply chain --> unsafe, reliability etc
• Length of Service /legacy: future potential value --> durability, reusable
• Design: provides the highest social value across the product life cycle for the longest duration
• Social value is the most important element of sustainable design
  • It needs to balanced with affordability/ profitability