2 (30) Orthotropic bone samples (12cm X 0.5cm X 2cm) having principal directions

Question

2 (30) Orthotropic bone samples (12cm X 0.5cm X 2cm) having principal directions of material symmetry 1-2 are cut from the same larger specimen. Application of loads in the horizontal direction results in the given deformed specimens shown in cases A and B below. .3%, .1905 a) Calculate v, and v2 b) Given that the applied load in Case Ais 35 kN, calculate the longitudinal and transverse moduli ,Soabp.7.Y/Epo c) Calculate the load applied in Case B d) Calculate the engineering and tensorial shear strains on the specimen in Case A at an angle of 30 ccw from the 1 direction. Draw a sketch of a material element that shows how the engineering shear strain deforms the material. _dV8 aad )-.0HR Case A 2.0cm 1.982c 12.28cm Case B2.0cm 1.99cm 12.315cnm Undeformed Deformed

Explanation / Answer

a) V12=2-1.982=0.018=18mm

V21=2-1.99=0.01=10mm

b) longitudinal moduli,

E1=35*1000*0.12/(0.02*0.005*0.0028)=15 GPa

Transverse moduli,

E2=0.02*35*1000/(0.02*0.005*0.0028)=625 MPa

c) load applied in case B,

P=15*0.02*0.005*0.00315/0.12=39.37 kN

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