problem4 - 22.314/1.56/2.084/13.14 Fall 2006 Problem Set IV...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 22.314/1.56/2.084/13.14 Fall 2006 Problem Set IV Due 10/12/06 1. Consider a cantilever beam with one end fixed into a wall. The dimensions are shown in the figure below. A force F = bhσy /2 is applied to the other end. σy is the yield strength. Now a bending moment is applied as shown in the figure. Determine the magnitude of the moment M at which the the beam fails. Assume idealized material law: elastic perfect plastic. M F L h b 2. The stress tensor can be written as the sum of a deviatoric stress tensor and a dilation stress tensor and the strain can be written as the sum of volumetric strain and deviatoric strain as follows: ⎡ ⎤⎡ ⎤⎡ ⎤ σ1 0 0 S1 0 0 −P 0 0 ⎣ 0 σ2 0 ⎦ = ⎣ 0 S2 0 ⎦ + ⎣ 0 −P 0 ⎦ 0 0 σ3 0 0 S3 0 0 −P ⎡ ⎤ ⎡� ⎤⎡ ⎤ �1 0 0 �1 0 0 �v /3 0 0 ⎣ 0 �2 0 ⎦ = ⎣ 0 ��2 0 ⎦ + ⎣ 0 �v /3 0 ⎦ 0 0 �3 0 0 ��3 0 0 �v /3 Where P = −(σ1 + σ2 + σ3 )/3 is the hydrostatic pressure and �v = �1 + �2 + �3 is the volumetric strain. Please show that the distortion energy UD is equal to: 3 1� � UD = Si �i 2 i=1 3. Consider several ceramic fuel materials with properties listed in the table below: Property Thermal conductivity average (W/mo C ) Melting point (o C ) Linear coefficient of expansion (/o C ) Fracture strength (MPa) 1 UO2 3.6 2800 10.1E-6 110 UC 23 2390 11.1E-6 60 UN 21 2800 9.4E-6 – (a) Calculate the theoretical maximum linear heat generation rate. (b) Compare the the minimum linear heat generation rates at which fracture would occur for UO2 and UC. 2 ...
View Full Document

Ask a homework question - tutors are online