I solved the principal stresses but having a hard time on determing the theta-P (orientation of principla plances), could you help me?

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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I solved the principal stresses but having a hard time on determing the theta-P (orientation of principla plances), could you help me?

Figure 9-42 Full Alternative Text
9-43. Determine the principal stresses in the box beam at point B. Show the results on an
element located at this point.
Prob. 9-43
2 ft-
10 kip
4 in.
A
6 in.
B
-1.5 ft-
4 in.
HA
B
4 kip
0.5 ft
13 in.
13 in.
-2 ft-
Transcribed Image Text:Figure 9-42 Full Alternative Text 9-43. Determine the principal stresses in the box beam at point B. Show the results on an element located at this point. Prob. 9-43 2 ft- 10 kip 4 in. A 6 in. B -1.5 ft- 4 in. HA B 4 kip 0.5 ft 13 in. 13 in. -2 ft-
Step 4)
Solve
Principal
Stresses
and
Orientation
Gin
6 (6)³ + (6) (6) (0)²
12
- [4 (4)² + (4) (4) (0)² ]
86-6666 in4
Iz=
·
5
Q = (1.9) ((6.3) - (4-2)) in ³
·19 in ³
=
T=VQ
It
= (2 kip) (19 in ³)
(86.6666m 4) (2 m)
Jx=0
OT
Jy=0
Txy=-0.2192 Ksi
01₁/2 = (J₂² +Jy) = √ (Tv=Jy)² + [ny²
Jx
Exy
= 0.2192 15.
= -0.2192 1sí
+ = ( 0 + ₂0 ) + √ ( 0 = 0 ) ² + (-0.2192je
2
O
B
02=
Op = 1/2 tan " ( _2 +Zxy)
Jx-Jy
EAS 212
Problem 1 Continued)
oz-(9)-J1=j+ (-0.? 3*
Т2=-0. 2192 ksi
-0.2192 Ksi
"error"
y =
y = 1. a in
Homework #8
(1.5.18)-(1.8)
18-8
Silva, Martin
C
Transcribed Image Text:Step 4) Solve Principal Stresses and Orientation Gin 6 (6)³ + (6) (6) (0)² 12 - [4 (4)² + (4) (4) (0)² ] 86-6666 in4 Iz= · 5 Q = (1.9) ((6.3) - (4-2)) in ³ ·19 in ³ = T=VQ It = (2 kip) (19 in ³) (86.6666m 4) (2 m) Jx=0 OT Jy=0 Txy=-0.2192 Ksi 01₁/2 = (J₂² +Jy) = √ (Tv=Jy)² + [ny² Jx Exy = 0.2192 15. = -0.2192 1sí + = ( 0 + ₂0 ) + √ ( 0 = 0 ) ² + (-0.2192je 2 O B 02= Op = 1/2 tan " ( _2 +Zxy) Jx-Jy EAS 212 Problem 1 Continued) oz-(9)-J1=j+ (-0.? 3* Т2=-0. 2192 ksi -0.2192 Ksi "error" y = y = 1. a in Homework #8 (1.5.18)-(1.8) 18-8 Silva, Martin C
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