Question: Wheres critical stress location Will it fail

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Question Wheres critical stress location? Will
it fail?
CASE 1 Torsion Load (Twisting Moment)
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Stress Analysis - Review

• Determine critical point
• Solve for internal forces at that point (or
  reduce to cantilever)
• Solve for stresses at that point
• Add like stresses
• Summarize stresses at that point on a stress
  element.
• May be necessary to use Stress Transformation or
  Mohrs circle to get max stresses!

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9.1 Stress Elements
a) Stress state for plane stress can be
summarized on a 2D element.
a) In general, can have 6 independent stresses (3
normal and 3 shear) acting at a point.
a) Many practical engineering problems involve
only three independent stresses called plane
stress.
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9.2 Plane Stress Transformation In this course
2D (use force equilibrium) Graduate course 3D
(use tensors!!)
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A. Given Plane Stress State
B. What are new stresses at element rotation of q
??
Note, positive stress directions shown.
Note, positive angle (ccw) shown.
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Easy, cut element, sum forces in the x and y
directions
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(9.1)
(9.2)
(9.3)
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9.3 Principal Stresses and Maximum In-Plane Shear
Stresses

• What are the maximum stresses at a point?
• Will they be different than whats shown on the
  initial stress element?

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Recall equation for normal stress at new angle q
(9.1)
Want max and min stresses so what do we do?
Solving for q
(9.4)
This is the principal plane
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Next, plug 9.4 into 9.1 and get
(9.5)
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So, to summarize
Principal Stress/Principal plane Note-shear
stresses are zero on principal plane!
(9.5)
(9.4)
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Next, do the same thing for shear stress
(9.2)
Solve for angle, then plug into eqn 9.2 to get
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(9.6)
(9.7)
(9.8)
1. On planes of max shear, normal stress is not
zero but savg as shown in 9.8. 2. The planes for
max shear stress can be determined by orienting
an element 45deg from the position of an element
of max principal stress!
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Summary
Max principal stress
Max shear stress
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