Question

Direct stresses of 120 N/mm^2 (tension) and 90 N/mm^2 (compression) are applied at a particular point in an elastic material on two mutually perpendicular planes the principal

stress in the material is limited to 100 N/mm^2(tension) calculate the allowable value of shear stress at the point on the given planes determine also the value of the other principal stress and the maximum value of shear stress at the point using Mohr's circle

Answer 1

$σx = 120MN/m2 (tensile i.e + ive)$

$σy = 90MN/m2$

$(Compressive i.e. – ive)$  

$τxy = ?$

$σ1 = 150MN/m2$  Since we have

$150 = ½[(120 – 90) + {(120 – (– 90))2 + 4(τxy)2}1/2]$

$τxy = 84.85MN/m2$  Now the magnitude of other principal stress

$σ2 σ2 = ½[(120 – 90) – {(120 – (– 90))2 + 4(84.85)2 }1/2]$

$σ2 = – 120MN/m2$  

The direction of principal planes is:

$tan 2θ = 2 τxy / (σx −σy)$  

$tan 2θ = (2 × 84.85)/(120 – (– 90))$

$2θ= 38.94º or 2218.94º θ$

$19.47º or 109.47º$