Hidden Label: left parenthesis, "S" Subscript, 1 , Baseline , 0 , right parenthesisS1,0
Label
equals=
left parenthesis, 59.7 0 0 2 7 4 7 , 0 , right parenthesis59.7002747,0
13
Hidden Label: left parenthesis, "S" Subscript, 3 , Baseline , 0 , right parenthesisS3,0
Label
equals=
left parenthesis, 23.2 9 9 7 2 5 3 , 0 , right parenthesis23.2997253,0
14
The values below are all the possible states of stress as a function of the Angle of Failure
15
Expression 16: left parenthesis, StartFraction, left parenthesis, "S" Subscript, 1 , Baseline minus "S" Subscript, 3 , Baseline , right parenthesis Over 2 , EndFraction , right parenthesis squared equals left parenthesis, "x" minus StartFraction, left parenthesis, "S" Subscript, 1 , Baseline minus "S" Subscript, 3 , Baseline , right parenthesis Over 2 , EndFraction minus "S" Subscript, 3 , Baseline , right parenthesis squared plus "y" squaredS1−S322=x−S1−S32−S32+y2
16
Expression 17: tangent left parenthesis, phi , right parenthesis "x" plus "a" Subscript, "c" , Baselinetanϕx+ac
17
Expression 18: "a" Subscript, "c" , Baseline equals 13ac=13
55
5050
18
Expression 19: phi equals 7.4ϕ=7.4
00
4545
19
The equations below are to aid you in visualizing the Mohr Circle. They serve no physical meaning, they just make it easier visualize the concept of the Mohr Circle
20
Expression 21: "x" equals "E" Subscript, 11 , Baselinex=E11
equals=
5656
21
Expression 22: StartFraction, negative "E" Subscript, 13 , Baseline Over left parenthesis, "E" Subscript, 33 , Baseline minus StartNestedFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis NestedOver 2 , EndNestedFraction , right parenthesis , EndFraction left parenthesis, "x" minus StartFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis Over 2 , EndFraction , right parenthesis left brace, StartFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis Over 2 , EndFraction less than "x" less than "E" Subscript, 11 , Baseline , right brace−E13E33−E33+E112x−E33+E112E33+E112<x<E11
22
Expression 23: StartFraction, "E" Subscript, 13 , Baseline Over left parenthesis, "E" Subscript, 33 , Baseline minus StartNestedFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis NestedOver 2 , EndNestedFraction , right parenthesis , EndFraction left parenthesis, "x" minus StartFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis Over 2 , EndFraction , right parenthesis left brace, StartFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis Over 2 , EndFraction less than "x" less than "E" Subscript, 11 , Baseline , right braceE13E33−E33+E112x−E33+E112E33+E112<x<E11
23
Expression 24: StartFraction, negative "E" Subscript, 13 , Baseline Over left parenthesis, "E" Subscript, 33 , Baseline minus StartNestedFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis NestedOver 2 , EndNestedFraction , right parenthesis , EndFraction left parenthesis, "x" minus StartFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis Over 2 , EndFraction , right parenthesis left brace, StartFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis Over 2 , EndFraction greater than "x" greater than "E" Subscript, 11 , Baseline , right brace−E13E33−E33+E112x−E33+E112E33+E112>x>E11
24
Expression 25: StartFraction, "E" Subscript, 13 , Baseline Over left parenthesis, "E" Subscript, 33 , Baseline minus StartNestedFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis NestedOver 2 , EndNestedFraction , right parenthesis , EndFraction left parenthesis, "x" minus StartFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis Over 2 , EndFraction , right parenthesis left brace, StartFraction, left parenthesis, "E" Subscript, 33 , Baseline plus "E" Subscript, 11 , Baseline , right parenthesis Over 2 , EndFraction greater than "x" greater than "E" Subscript, 11 , Baseline , right braceE13E33−E33+E112x−E33+E112E33+E112>x>E11