a ForceInternal Forces

Gevelyn Bontilao Itao, MOE

Mindanao State University Iligan Institute of Technology

College of Engineering

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Internal Forces

Objectives:The design of any structural or mechanical member requires an investigation of the loading acting within the member in order to be sure the material can resist the external loadings applied into it..

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Internal Forces

The internal loadings ca be determined using the method of sections.

If internal loadings at the cross-section of C are to be determined an imaginary line is passed thru the beam, cutting it into two segments.

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Internal Forces

Rectangular force components are developed to maintain equilibrium: N – force component acting normal to the beam V – force component acting tangent to the beam M – couple moment; bending moment

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Internal Forces

N, V, and M must be equal in magnitude but opposite in directions on each segent (Newton’s 3rd Law)

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Internal Forces

Vx , Vz – shear force components (tangent to the section) Ny – normal force (axial) Mx , Mz – bending moment My – tortional moment/twisting moment (motion is along the axis perpendicular to the section)

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Internal Forces

Example 1:The beam is supports the loading shown. Determine the internal normal force, shear force and bending moment acting just to the left of point C and just to the right of point C.

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Internal Forces

Example 2:Determine the internal normal force, shear force and bending moment acting at point B of the two-member frame shown.

a ForceShear and Moment Diagrams

Gevelyn Bontilao Itao, MOE

Mindanao State University Iligan Institute of Technology

College of Engineering

gsbitao_2013

Shear and Moment Diagrams

Objectives:The design of beam requires an investigation of the shearing forces and bending moments produced by the load in order to be sure the beam can withstand the external loadings applied into it.

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Shear and Moment Diagrams

Classification of Beams: Based on the type of supports

1. SIMPLY SUPPORTED BEAMS – pinned at one end and roller at the other end.

2. Cantilever Beam – fixed support at one end and free on the other end.

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Shear and Moment Diagrams

Variation of V and M is a function of the position x along the beam’s axis.

The function describing the variation of V and M become discontinuous where distributed load changes or where concentrated loads or couple moments are applied

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Shear and Moment Diagrams

Sign Convention:Positive directions: V – cause clockwise rotation of the member on which

it acts M – causes compression or pushing on the upper part

of the member. If the beam is elastic, M would tend to bend the member, concave upward.

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Shear and Moment Diagrams

Procedure for Analysis:1. Determine all the reactive forces and couple moments

acting on the beam and resolve all the forces into components acting perpendicular and parallel to the beam’s axis.

2. Specify separate coordinates x having an origin at the beam’s left end and extending to the regions of the beams between concentrated forces and/or couple moments and draw the FBD’s of the sections.

3. Shear is obtained by summing forces perpendicular to the beam’s axis.

4. The moment is obtained by summing moments about the sectioned end of the segment.

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Shear and Moment Diagrams

Example 1:Draw the shear and bending moment diagrams for the shaft shown. The support at A is a thrust bearing and the support at C is a journal bearing.

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Shear and Moment Diagrams

Example 2:Draw the shear and bending moment diagrams for the beam shown.