8/18/2019 Tutorial 01 - Stress-strain

1/2

Tutorial 1: Stress & Strain

Question 1: The oldest surviving obelisk, standing in Heliopolis, Cairo, is a stone column of height 20 m and approximately constant square cross-section !" m by !" m! #f thedensity of the red granite from $hich it is carved is 2%&0 kg'm ( , determine the axialstress at) a* the very top of the column+ b* the base of the column, using theaccepted sign convention!

Question 2: The longest bone in the human body, the femur or thigh bone, is typically 0! mlong and a$ay from the hip and knee oints is an approximately cylindrical tube of external diameter 0!0( m and $all thickness . mm! #f the maximum compressivestress of bone is 2. / 'm 2 , and allo$ing a factor of safety n of 2, $hat mass $ouldyou be able to carry on your shoulders if your femurs $ere the limiting load-bearingstructure in your body1 #f the elastic modulus E of bone is 3 'm 2 , by ho$ much$ould your femurs shorten1 4isregard your o$n body mass!

Question 3: The main ski lift at 5he6eld 5ki 7illage is a 8button lift9 : each skier grasps a pole,the bottom of $hich is a button $hich supports the body, and the top of $hich isconnected to the lift cable system! #f the pole has an external diameter of 0!0( m, a$all thickness of mm, a length of ( m, and can be considered to be in uniaxialtension of "00 , determine) a* the axial stress+ b* the axial strain+ c* theelongation+ and d* the change in diameter of the pole, if it is manufactured from

202 aluminium alloy ;< = 3>a,v

= 0!(*!

Question 4: The rectangular plate is sub ected to the deformation sho$n by the dashed line!4etermine the average shear strain xy of the plate and normal strain of ?@!

Question 5: The rectangular plate is sub ected to the deformation sho$n by the dashed lines!4etermine the average shear strain xy of the plate! 4etermine the average normalstrains along the diagonals ?C and side ?@!

8/18/2019 Tutorial 01 - Stress-strain

2/2