ES 13 Lecture 11

Combined Loading

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Stresses that we know so far…Normal Stress

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Pure Shear Stress

Torsional Shear Stress

Bending Stress

Transverse Shear Stress

What if…ES 13M

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Internal Forces DevelopedES 13M

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Corresponding Stresses Developed ES 13M

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Assumptions for AnalysisES 13M

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1. Stresses < Proportional Limit (Elastic)

2. Member geometry should NOT undergo significant change

3. Section analyzed is far from the points of application of loads

Example 11.1ES 13M

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The rectangular block of negligible weight is subjected to a vertical force of 40 kN applied to its corner. Determine the largest normal stress acting on a section through ABCD.

Example 11.1ES 13M

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Replacing the single force by a system acting at the center,

Example 11.1ES 13M

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Normal Stress:

Bending Stress about X:

Bending Stress about Y:

Example 11.1ES 13M

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By Superposition,

Example 11.2ES 13M

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Two forces P1 and are applied as shown to the end A of bar AB, which is welded to a cylindrical member BD of radius c = 20 mm.

Determine the normal and shearing stresses at point K of the transverse section of member BD

Example 11.2ES 13M

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Example 11.2ES 13M

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Normal Stress σ at K:

Example 11.2ES 13M

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Shearing Stress τ at K:

Example 11.2ES 13M

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Shearing Stress τ at K:

Quiz #11.1 ES 13M

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Knowing that the cross section containing point H is a 20 x 40-mm rectangle, determine normal and shearing stress at point H.

Quiz #11.2 ES 13M

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Determine w for the following allowable stresses:Axial Stress = 13.5 MPaTransverse Shear Stress at NA = 900 kPaTransverse Shear Stress at Junction = 800 kPa

Example 11.3ES 13M

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The bar has a diameter of 80 mm. Determine the stress components that act at point B.

Example 11.3ES 13M

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Example 11.3ES 13M

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Normal Stress σ at B:

Example 11.3ES 13M

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Shearing Stress τ at B

Example 11.3ES 13M

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Shearing Stress τ at B

Example 11.4ES 13M

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Determine the shortest distance d to the edge of the plate at which P can be applied so that it produces no compressive stresses on the plate at section a–a. The plate has a thickness of 10 mm and P acts along the center line of this thickness.

Example 11.4ES 13M

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MP

Assuming d > 100 mm,

Compressive stress can only happen at the RIGHT of the NA

Example 11.4ES 13M

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MP

Assuming d < 100 mm,

Compressive stress can only happen at the LEFT of the NA

Example 11.5ES 13M

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Three steel plates, each 13 mm thick, are welded together to form a cantilever beam. For the loading shown, determine the normaland shearing stresses at points a and d. Beer 8.53

Quiz # 11.3ES 13M

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Knowing that the tension in the cable is 40 kN, determine the MAXIMUM normal stresses at SECTION H. Beer 8.38