Question

(b) Explain the usefulness of Mohr's Circle in engineering context and discuss the advantages of Mohr's circle. Quote any references. [15 marks] B 80 mm 100 mm P T Figure 1: A-36 steel pipe with loadings.

Answer 1

Moht circle - (brief introduction)

inplane riman 7 = 6% The Last Case 1 2 on + Refrence plane 0,462,6-02] 2=0/0 F Train Plane 100st) (0,012) 4 A(0,0%) Minor Principal Plane MGX Comp 54.pleme omania E LT TR on Twarplane planen 0/52. ve) DC01,0)= (167)mek, 0) <o O Dedi (0,0) le (8/210) major principal plane Plane of Purl Shear 202 07 Max-tensile stess Plane br (0,-) zero Wormalst copies > Zmax Plane " ( 0782, - (0* vel

With the help of Mohr circle we can calculate various state of stresses on an element by knowing very few about it. This gives us an advantage as we can see the below conclusions -

ବ Conclusions from Mohr Circle- 0 Any plane passing through a point in Represented in the more circle by a Radial line. Plane Passing through a point is represented .en the monere ciocle by couble its actual angle. (28) XBY wordinates of any point on the mour Circle Represents Normal o Shear Shess on the corresponding Every prene Respectively. on the 4 contre of Mohr little always lies on X-9xis. 15,482,0] 6 Principal planes are the Radial lines lying X-9x15 © Principal stresses are equal to X-Coordinates of points intersection of circle with X-axis. © Diameter of hoher Circle is equal to difference of major minor principal stresses - (p= 01-03] ® ? may planes are the Radical lines Pallared to Yaxes. a Normal stress on tmax planes cont) is equal to x coordinate of caute of nowher Grello ① In plane Zmax Radius of noha Circle. = +R = (01-02) = the Joyroyje tering

Planes of pure shear will exist on when mone Civele intueseet yours ( when Principal stresses are Unlike in natwu) (12) Planes Pure shear are the Radial eines Passing through the points where Circle interseets oy Y auis. 17 of ④ Resultant stress on any oblique plane is equal to length of the line which is joining corresponding point on the circle with the origine when mour colle intersect tot yaxis, then absolute Tmax is equal to Radius that circle. Mohr Circle may become tangential to yanis ( Linder imia vial state of stress) but It will be Nwer tangential to y -axis • 16 Refrence plane may lie on x-axis 60 y-cixis con An may lie in any of the quadbrents. © when major & minor principal stresses vre equal o Canlusions can be unlike in nature, the following made (0) Tmax plane & Planes of Pure shear winside with fach other. (11niche circle is a Circle with origin as a contie. = In Plane may Alb Tmax 110) arst resultant Shen on any oblique Plane • Radius of why circle. (6 c) may

And Mohr circle can be constructed for any second order tensor such as stress, strain, moment of inertia etc.

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