PCalc and HP 50g: Mohr's Circle

Given shear stresses in the x and y directions (σx and σy) and normal stress (τ), find the radius, center, and viewing angle of Mohr's Circle.

I take τ to represent both τxy and τyx (both are assumed to be equal).

Radius:

R = √( (σx - σy)/2)^2 - τ^2 )

Center (S, 0):

S = (σx + σy)/2

Viewing Angle:

θ = atan( 2τ /(σx - σy)) / 2

Sources:

HP 35S Program by Jason Charalambides, Avant Garde Engineering. HP 35S program written in 2012.

http://www.avant-garde-engineering.com/HP35s_Programs/Mohr's%20Circle.pdf

Wikipedia Article on Mohr's Circle, retrieved 5/23/2014:

http://en.wikipedia.org/wiki/Mohr's_circle

PCalc:

Before running, store the following values:

σx into M1

σy into M2

τ into M3

Program: Mohr's Circle - Radius

Decimal Mode

Set X To M1

Subtract M2 From X

Divide X By 2

X To Power of 2

Set R0 To M3

R0 To Power of 2

Add R0 To X

X To Power of 0.5

Program: Mohr's Circle - Center (X,0)

Decimal Mode

Set X To M1

Add M2 To X

Divide X By 2

Program: Mohr's Circle - View Angle

Decimal Mode

Set X To M3

Multiply X By 2

Set R0 To M1

Subtract M2 From M0

Divide X By R0

Inverse Tangent X

Divide X By 2

HP 50g: MOHR

σ: ALPHA, Right-Shift, S

τ: ALPHA, Right-Shift, U

SQ: x^2

<< "Shear Stress σx" PROMPT

"Shear Stress σy" PROMPT

"Normal Stress τ" PROMPT

→ X Y T

<< X Y - 2 / SQ T SQ + √

"Radius" →TAG

X Y + 2 / (0,0) +

"Center" →TAG

T 2 * X Y - / ATAN 2 /

"View Angle" →TAG >> >>

Example:

σx = 100

σy = -220

τ = 80

Results:

R ≈ 178.88544

S = -60 (center (-60,0))

θ ≈ 13.28253° ≈ .23183 radians

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