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ENGR 225 Section

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**Mechanics of Materials**

Mechanics of Solids Mechanics of Deformable Bodies Solid Mechanics Strength of Materials.

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Statics Forces Rigid Bodies Dynamics Motion Particles, Rigid Bodies Mechanics of Materials Forces External Internal Material Properties

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**Mechanics of Materials**

Area of mechanics that studies the relationships between external loads applied to a deformable body and the intensity of internal forces within a body An understanding of material behavior will play an important role in developing the necessary equations used in mechanics of materials.

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Support Reactions

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Internal Forces

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Method of Sections

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Internal Forces in 2-D

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Determine the internal forces (normal force, shear force and bending moment) on a section passing through the beam at point C.

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Internal Forces in 3-D

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**Internal Forces in 3-D Find the internal forces at the base**

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**Mass = 650 kg and Wind Load = 900 N/m2**

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**Internal Forces at a point – method of Sections**

Internal forces at all points along length Internal forces – a function of distance along length of beam.

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**Shear and Moment Diagrams**

For beams we can calculate the shear and moment diagrams as a function of position along the beam. Internal normal force will not be considered in that most loadings are vertical on a beam and we are primarily concerned about shear and bending failures.

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Sign Convention Shear ~ positive direction is denoted by an internal force that causes a clockwise rotation on which it acts. Moment ~ positive direction is denoted by an internal moment that causes a compression or pushing on the upper part of the member

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**Relations between Distributed Load, Shear, and Moment.**

Slope of the Shear Diagram = Negative of distributed load intensity Slope of the bending moment diagram = Shear

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**Graph the internal forces shear force and bending moment along the axis of the beam.**

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