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Transcript of MAE 241 - Lec10
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MAE 241 - Statics
Summer 2009
Dr. Konstantinos A. Sierros
Office Hours: M and W 10:30 – 11:30 (263 ESB new add)
Teaching Blog: http://wvumechanicsonline.blogspot.com
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Determine the force in each member of the truss andstate if the members are in tension or compression. Set P1
= 2 kN and P2 = 1.5 kN.
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Determine the force in members JI and DE of the K truss. Indicate if the
members are in tension or compression.
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The truck and the tanker have weights of 8000 lb and 20000 lb respectively. Their respective centers of gravityare located at points G1 and G2 .
If the truck is at rest, determine the reactions on bothwheels at A, at B, and at C. The tanker is connected to thetruck at the turntable D which acts as a pin.
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Chapter 7: Internal forces
Chapter objectives• Use the method of sections to determine
internal loadings in a member • Generalize the procedure in order to
formulate equations that can be plotted to
describe internal shear and moment
throughout a member • Analysis of forces and geometry of
cables supporting a load
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7.1 Internal forces developed in structural members
•To design a structural or mechanical member it is necessary to know
the loading acting within a member in order to make sure the materialcan resist this loading• Internal loadings can be determined by using the method of sections• Use section B, separate the beam into two segments. The internal
loadings acting at B will then become external
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7.1 Internal forces developed in structural members
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• NB acts perpendicular to the cross-section and is termed the normal
force
• VB is tangent to the cross-section and is called shear force• MB is bending moment
• The force components prevent the relative translation between the
two segments. The couple moment prevents the relative rotation
• When analysing forces/moments the right segment is the better choicesince it doesn’t involve the unknown reactions at A
7.1 Internal forces developed in structural members
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7.1 Internal forces developed in structural members
Normal force (N) is positive when creates
tension
A positive shear force (V) will rotate thesegment clockwise
A positive bending moment will tend to bend
the segment in a concave upward manner
(smiley face)
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7.2 Shear and moment equations and diagrams
• Beams are structural members designed
to support loadings applied perpendicular
to their axes• Simply supported beam is pinned at one
end and roller supported at the other • Detailed knowledge of the variation of
the internal shear force V and bendingmoment M along the beam axis
• Using the method of sections we can find
these variations