HP 50g Graphing, 48gII Graphing manual Mohr’s Circle 14, Example

Equations:

σ x1 = σ

τx 1y 1

x + σ y + σ x – σ y ⋅ COS (2 ⋅ θ ) + τxy ⋅ S IN(2 ⋅ θ )

2 2

σx 1 +σ y 1 = σ x + σ y

σ x – σ y	⋅ S IN(2 ⋅ θ ) + τxy ⋅ σ y
= –2 

Example:

Given: σx=15000_kPa, σy=4755_kPa, τ xy=7500_kPa, θ=30_°.

Solution: σx1=18933.9405_kPa, σy1=821.0595_kPa, τ x1y1= 686.2151_kPa.

Mohr’s Circle (14, 4)

Equations:

σ 1 =	σ-----x-----+-----σ----y--	+	σ-----x-----–----σ-----y-	+ ρxy2
	2		2

σ1 + σ 2 = σ x + σ y

SIN(2 ⋅ θ p1) = -------	τxy
	σ-----x-----–----σ--------y---		2-------------------

	----------2----------		+ τxy
θ p2 = θ p1 + 90			τmax =		σ-----1-----–----σ-----2-
					2
θ s = θ p1 – 45			σ avg =		σ-----x-----+-----σ----y--
					2
Example:
Given: σx=5600_psi, σy=18400_psi,				τ xy=4800_psi.
Solution: σ1= 4000_psi, σ2= 20000_psi,					θp1=18.4349_°, θp2=108.4349_°, τ max=8000_psi,
θs= 26.5651_°, σavg= 12000_psi.

558 Equation Reference