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Chapter 4

Internal Loadings Developed in Structural Members

Iqbal Marie

2018-2019

Hibbeler, R. C., Structural Analysis, 7th Edition,

Internal loading at a specified Point

The internal forces in structural members (coplanar structure) are:Normal force N,Shear force V,Bending moment M.

+ve Sign

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Procedure For Analysis

FBD and find Support Reactionto be calculated before determining the Internal Loadings

Section where internal loadings are requiredPass Section perpendicular to its axis at the specified pointWith all the external loading ( distributed, moments and concentrated

forces)in their exact location for either part of the section.

Free Body Diagram ( of either part of the section)Draw FBD of the simplest segment which is with the least number of loadsIndicate the unknowns ( in their positive signs)( N , V and M ) in their positive direction

Equations of EquilibriumIf the solution of equilibrium equations yields negative value then the sense of the

internal loading is opposite to the assumed(-) Internal Loadings Opposite Direction

The 9 kN force is supported by the floor panel DE which in turn is simply supported at its ends by floor beams. These beams transmit their loads to the simply supported girder AB. Determine the internal shear and moment acting at point C in the girder.

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Shear and Moment function

Procedure for Analysis:

1- Support reaction2- Shear & Moment Function

• Specify separate coordinate x and associated origins, extending into regions of the beam between concentrated forces and/or couple moments or where there is a discontinuity of distributed loading.

• Section the beam at x distance and from the free body diagram determine V and M at section x as a faction of x

Determine the shear and moment in the beam as a function of X

X=12m

X=12m

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4.3 Shear and Moment diagram for a Beam

When F acts downward on the beam, ΔV is negative so that the shear diagram shows a “jump” downward.If F acts upward, the jump is upward.

If an external couple moment M’ is applied clockwise, ΔM is positive, so that the moment diagram jumps downward,And when M’ acts counterclockwise, the jump must be upward.

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Inclined Beam

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4.4 Shear and Moment diagrams for Frames

Draw Normal, shear and moment diagrams

ReactionsFBD for each element

SD and MD

Draw the shear and moment diagrams for the frame shown . Assume A is a pin,C is a roller,.

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4.5 Moment diagram constructed by the method of superposition