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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Presentation transcript:

Ch 1 Sec 3,4,5 Definition of Stress – Sec 3 Average Normal Stress – Sec 4 Average Shear Stress – Sec 5

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!!! S of M!! STATICS!!

Definition of Stress: Internal Force per unit area Intensity of internal force on a specific plane (area) passing through a point 1-3

This is a 3D stress element. Can have up to 6 independent stresses at a point (graduate level)

3.4 Average Normal Stress: a. External Force b. Internal Force c. Stress

3.4 Average Normal Stress: Normal Stress (psi, ksi, Mpa) Internal Load (lbs, K, N, kN) Cross-sectional Area (in 2, mm 2, m 2 )

3.4 Average Normal Stress: Stress profile – uniform across cross-section. Note, static equilibruim applies  *A = F

3.4 Average Normal Stress:

Requirements for Average Normal Stress,  = P/A: 1.Member starts out straight and remains straight after loading 2.Homogenous, isotropic 3.Invoke St. Venant’s Principal EXAMPLES of AVERAGE NORMAL STRESS: 3.4 Average Normal Stress:

Example Normal Stress: If P = 20K lbs and A = 2 in 2  = ? Do other examples!

Statics done, now what are stresses in each segment??

Average Normal Stress (tension) P P Average Normal Stress (comp)

3.5 Average Shear Stress: Internal load, V Stress, 

3.4 Average Shear Stress: Shear Stress (psi, ksi, Mpa) Internal Load (lbs, K, N, kN) Total Shear Area (in 2, mm 2, m 2 )

3.5 Average Shear Stress:

If load = 2,000 lb and bolt diameter = ½”, Find shear stress in bolt. Example Shear Stress:

3.5 Average Shear Stress: Stress type = ?? Single or Double??

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3.5 Average Shear Stress: Key, all 4 shear stresses are equal in magnitude!!

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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. Side: what is the shear stress in pin and bending stress in handle? SofM Do this for homework. See solution Link

Statics: Example 2 – Crane Structure Given: Crane structure as shown. Find: Forces and FBD’s for cables A-B and A-E, boom DEF and post AFC. Side: what is the normal stress in cables (average normal only) and normal stress in boom and post (combined loading)? SofM Do this for homework. See solution Link

Statics: Example 3 – Truss Structure Given: Truss structure as shown. Find: Forces in each member: AB, BC, AD, EF, BD, BE, CE, CF Side: what is the normal stress in each truss member (away from joints)? SofM Do this for homework. See solution Link