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Combined Stresses and Mohr Circle

Concept Concept Concept Concept Concept

Combined Stresses Visualized

A beam can be subjected to multiple stresses at once—axial normal stress, bending normal stress, torsional shear, and transverse (horizontal) shear. In the linear-elastic range, evaluate each at the same point and add them (superposition) for the net state.

$$ \sigma = \frac{P}{A} $$

$$ f_b = \frac{M c}{I} $$

$$ \tau_{\text{torque}} = \frac{T r}{J} $$

$$ \tau_{\text{shear}} = \frac{V Q}{I b} $$

Concept Concept Concept Concept

Problem: Cast-Iron with Axial and Bending Stresses

A cast iron is shown below. The allowable stresses are 30MPa in tension and 70MPa in compression.
a. Determine the safe value of P (in kN) based on the allowable tensile stress.
b. Determine the safe value of P (in kN) based on the allowable compressive stress.

Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 1: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 1: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 1: – Diagram

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 1: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 1: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 1: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 1: – Diagram

Problem 2:

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 2: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 2: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 2: – Diagram

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 2: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 2: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 2: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 2: – Diagram

Problem 3:

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 3: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 3: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 3: – Diagram

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 3: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 3: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 3: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 3: – Diagram

Problem 4:

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 4: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 4: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 4: – Diagram

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 4: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 4: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 4: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 4: – Diagram

Problem 5:

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 5: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 5: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 5: – Diagram

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 5: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 5: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 5: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 5: – Diagram

Problem 6:

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 6: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 6: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 6: – Diagram

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 6: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 6: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 6: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 6: – Diagram

Problem 7:

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 7: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 7: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 7: – Diagram

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 7: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 7: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 7: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 7: – Diagram

Problem 8:

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 8: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 8: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 8: – Diagram

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Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 8: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 8: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 8: – Diagram Combined Stresses & Mohr Circle | Mechanics of Deformable Bodies – Problem 8: – Diagram
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