1. Mindanao State University
Iligan Institute of Technology
College of Engineering
Internal Forces
a Force
Gevelyn Bontilao Itao, MOE

2. 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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3. 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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4. 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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5. 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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6. 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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7. 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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8. Internal Forces
Example 2:
Determine the internal normal force, shear force and
bending moment acting at point B of the two-member
frame shown.
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9. Mindanao State University
Iligan Institute of Technology
College of Engineering
Shear and Moment Diagrams
a Force
Gevelyn Bontilao Itao, MOE

10. 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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11. 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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12. 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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13. 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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14. 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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15. 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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16. Shear and Moment Diagrams
Example 2:
Draw the shear and bending moment diagrams for the
beam shown.
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