Ch 1 Sec 3,4,5

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Ch 1 Sec 3,4,5

• Definition of Stress Sec 3
• Average Normal Stress Sec 4
• Average Shear Stress Sec 5

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Ch 1 Sec 3,4,5

• Recall Strength of Materials Problem
• Solve for unknown ext loads
• Solve for required internal loads
• Solve for required area properties
• Internal loads produce stress, strain,
  deformation!!!

STATICS!!
S of M!!
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1-3

• Definition of Stress
• Internal Force per unit area
• Intensity of internal force on a specific plane
  (area) passing through a point

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1-3
This is a 3D stress element. Can have up to 6
independent stresses at a point (graduate level)
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3.4 Average Normal Stress
b. Internal Force
a. External Force
c. Stress
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3.4 Average Normal Stress
Internal Load (lbs, K, N, kN)
Cross-sectional Area (in2, mm2, m2)
Normal Stress (psi, ksi, Mpa)
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3.4 Average Normal Stress
Stress profile uniform across cross-section.
Note, static equilibruim applies sA F
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3.4 Average Normal Stress
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3.4 Average Normal Stress

• Requirements for Average Normal Stress, s P/A
• Member starts out straight and remains straight
  after loading
• Homogenous, isotropic
• Invoke St. Venants Principal

EXAMPLES of AVERAGE NORMAL STRESS
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3.4 Average Normal Stress
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Example Normal Stress
If P 20K lbs and A 2 in2 s ?
Do other examples!
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Statics done, now what are stresses in each
segment??
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Average Normal Stress (tension)
P
P
Average Normal Stress (comp)
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3.5 Average Shear Stress
Internal load, V
Stress, t
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3.4 Average Shear Stress
Internal Load (lbs, K, N, kN)
Total Shear Area (in2, mm2, m2)
Shear Stress (psi, ksi, Mpa)
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3.5 Average Shear Stress
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Example Shear Stress
If load 2,000 lb and bolt diameter ½, Find
shear stress in bolt.
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3.5 Average Shear Stress
Stress type ?? Single or Double??
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3.5 Average Shear Stress
Double shear is better!! ½ the stress at the same
load since two areas carry load in shear!!
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3.5 Average Shear Stress
Key, all 4 shear stresses are equal in magnitude!!
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3.5 Average Shear Stress
Section a-a vs section b-b understand the
concept!!
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Statics Example 1 - Pliers
Given Typical household pliers as shown. Find
Force applied to wire and force in pin that
connects the two parts of the pliers.
Do this for homework. See solution Link
Side what is the shear stress in pin and bending
stress in handle? SofM
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Statics Example 2 Crane Structure
Given Crane structure as shown. Find Forces and
FBDs for cables A-B and A-E, boom DEF and post
AFC.
Do this for homework. See solution Link
Side what is the normal stress in cables
(average normal only) and normal stress in boom
and post (combined loading)? SofM
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Statics Example 3 Truss Structure
Given Truss structure as shown. Find Forces in
each member AB, BC, AD, EF, BD, BE, CE, CF
Do this for homework. See solution Link
Side what is the normal stress in each truss
member (away from joints)? SofM