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Average Shear Stress

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الكلية كلية الهندسة/المسيب     القسم هندسة السيارات     المرحلة 2
أستاذ المادة علي حسين عبيد محمد عجام       23/10/2019 06:39:58
Average Shear Stress
Shear stress is the stress component that acts in the plane of the sectional area. Consider a force F acting on the bar shown, if the
Supports are rigid and the force is large enough,
the material of the bar will deform and fail along
the planes AB and CD.
By drawing a free-body-diagram for the unsupported
center segment of the bar show that V=F?2
the Average shear stress distributed over each area is
?_avg=V/A
?_avg is average shear stress at the section, assumed to be the same at each point located in the section
V is the internal resultant shear force on the section determined from the equation of equilibrium.
A is the area at the section.
?_avgis in the same direction of V .
(this loading case is an example of Simple or Direct Shear stress. This type occurs at simple connections that use bolts, pins, welding materials. However, this equation is approximate).
Shear stress Equilibrium
If we take a volume element at a point on the surface subjected to a shear stress ?zy, the force and moment equilibrium requires ?zy to accompanied by shear stresses acting on three other cases (? zy , ?yz , ? yz). Using equations of equilibrium we will show that these stresses are equal:






???F_y=0 ?_zy (?x?y)-?_zy^ (?x?y) ?=0 ?_zy=?_zy^
???F_z=0 ?_yz (?x?z)-?_yz^ (?x?z) ?=0 ?_yz=?_yz^
???M_x=0 ?-?_zy (?_x ?_y ) ?_z+?_yz (?_x ?_z ) ?_y =0 ?_zy=?_yz
So that ?_zy=??_zy^ =??_yz=?_yz^ =?
In other words, all four shear stresses must have equal magnitude and be directed either toward or away from each other at opposite edges of the element. The material in condition shown above is subjected to a pure shear.


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