Chapter 1-3 Essentials

 

 

 

 

 

axial σ = N/A τ = V/A Hooke's law, stress-strain curves σ = Eε τ = Gγ stress transformations strain transformations ε = δ/L δ = NL/EA + αΔTL φ = TL/GJ M = EI d2y/dx2 torsion τ = Tc/J flexure σ = -My/I shear τ = VQ/Ib pressure σ = pr/t σ = pr/2t

 

 

 

normal stress/strain		σaxial	=	N / A
		εaxial	=	ΔL / Lo
		εtransverse	=	Δd / d
		Pressurex contact points beam compression				beam flexure pin and roller cantilever  formula sheet
shear stress/strain		τcutting	=	V / A
		γ	=	Δangle
		double shear test video      more shear examples
bearing stress		σb	=	Fb / Ab
		bearing examples   dowel bearing test video post bearing test 1 video post bearing test 2 video

 

Hooke's Law

σ

=

Eε

 

 

stress-strain diagrams

• modulus of elasticity, E = slope of intial linear part of the stress-strain curve
• proportional limit stress, σ_pl = stress value at which the stress-strain curve goes nonlinear
• yield point stress, σ_y = stress value at which the stress-strain curve goes horizontal (for many steels)
• 0.2%-offset yield stress, σ_{0.2% yp} = the stress value at which a line drawn with slope E starting at 0.002 strain intersects the stress-strain curve
• ultimate tensile stress, σ_ult = largest stress on the stress-strain curve (top of the curve)
• engineering fracture stress = fracture load / original area
• true fracture stress = fracture load / fracture area
• energy at yield = area under the elastic portion of the load-deformation curve
• energy at break = area under the entire load-deformation curve
• modulus of resilience, U_r = area under the elastic portion of the stress-strain curve = σ_pl² / 2E = the amount of energy (or work) stored per unit volume at the elastic limit
• modulus of toughness, U_t = area under the entire stress-strain curve = the amount of energy absorbed per unit volume at fracture -- a measure of the material ductility
• percent elongation = (L_f - L_o) / L_o x 100%
• Percent Elongation of 2" Gage Length = ΔL₂ / 2" x 100%
• Percent Elongation of 8" Gage Length = ΔL₈ / 8" x 100%

• percent reduction in area = (A_f - A_o) / A_o x 100%

 

survey

props: pipe

props not used: 

• pressurex sample
• play-doh
• Roark text
• hammer, board, nails
• cheese sticks
• loaf of bread
• round cookie cutter
• sheets of paper
• string cheese -- how many ways can you break it by hand? -- are your hands clean?
• paper -- how many ways...
• string cheese in stronger blocks
  • broken polymer tension samples to hold cheese sticks
  • single, double shear
• carrot in sliced bread holes
  • bearing stress
• http://www.youtube.com/watch?v=jqFoHaGtkig