Solid Mechanics (002)
Quiz 2
Student #
Name
:
:
1. Two members of uniform cross section 50 × 80 mm are glued together along plane a-a that forms
an angle of 25° with the horizontal. Knowing that the allowable stresses (normal stress: σ, shear
stress: τ) for the glued joint are σ = 800𝑘𝑃𝑎 and τ = 600 𝑘𝑃𝑎, determine the largest centric load P
that can be applied.
Problem 1
2. The strains determined by the use of the rosette shown during the test of a machine element are
−6
ϵ1 =+ 600×10
−6
ϵ2 =+ 450×10
−6
ϵ3 =− 75×10
Determine (a) the in-plane principal strains, (b) the in-plane maximum shearing strain.
Problem 2
Solid Mechanics (002)
3. A cylindrical thin-walled storage tank used to transport gas under pressure has an inner diameter of
60 cm and a wall thickness of 1.8cm. Strain gages attached to the surface of the tank in transverse and
−6
longitudinal directions indicate strains of (1) 255×10
−6
and (2) 60×10
cm/cm, respectively.
Knowing that a torsion test has shown that the shear modulus of the material used in the tank is
𝐺 = 77 𝐺𝑃𝑎, determine (a) the internal pressure in the tank (assume that the external gas
pressure is 0 GPa), (b) and the maximum in-plane shear stress in the wall of the tank.
Problem 3
- 𝑠ℎ𝑒𝑎𝑟 𝑚𝑜𝑑𝑢𝑙𝑢𝑠: 𝐺 =
𝐸
2(1+ν)
- 𝑠𝑡𝑟𝑒𝑠𝑠 − 𝑠𝑡𝑟𝑎𝑖𝑛 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 : ϵ𝑖 =
1
𝐸
[σ𝑖 − ν(σ𝑗 − σ𝑘)]
'
τ = 𝐺γ
'
(ν: 𝑝𝑜𝑖𝑠𝑠𝑜𝑛 𝑟𝑎𝑡𝑖𝑜, 𝐸: 𝑌𝑜𝑢𝑛𝑔 𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠, 𝐺: 𝑆ℎ𝑒𝑎𝑟 𝑀𝑜𝑑𝑢𝑙𝑢𝑠)