ROMBLON STATE UNIVERSITY
COLLEGE OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF CIVIL ENGINEERING
MODULE 3
Internal Loadings Developed in
Structural Members
STRUCTURAL THEORY
Course Description: A professional course common to all
civil engineering students designated to provide
fundamental concepts, principles, and theories in the
theory of structures and structural analysis for internal
actions in structure and its deformations under load
ENGR. APRILLE ANN M. SIM
MODULE 3 INTERNAL LOADINGS AT A SPECIFIED POINT
The internal load at a specified point in a member
Internal Loadings Developed in can be determined by using the method of
sections. In general, this loading for a coplanar
Structural Members structure will consist of a normal force N, shear
force V, and bending moment M. It should be
Overview realized, however, that these loadings actually
Before a structural member can be proportioned, it represent the resultants of the stress distribution
is necessary to determine the force and moment acting over the member’s cross-sectional area at
that act within it. In this module we will develop the the cut section. Once the resultant internal
methods for finding these loadings at specified loadings are known, the magnitude of the stress
points along a member’s axis and for showing the can be determined provided an assumed
variation graphically using the shear and moment distribution of stress over the cross-sectional area is
diagrams. Applications are given for both beams specified.
and frames. Sign Convention
Learning Outcomes: Before presenting a method for finding the
internal normal force, shear force, and bending
APPLY the methods of structural analysis for external
moment, we will need to establish a sign
and internal actions on various types of structural
convention to define their “positive” and
systems due to static and moving loads.
“negative” values. Although the choice is
Learning Objectives arbitrary, the sign convention to be adopted here
Student Upon completion of this module, has been widely accepted in structural
Learning you will be able to: engineering practice, and is illustrated in Fig. a.
Objectives for Determine the different internal On the left-hand face of the cut member the
this Module loadings developed in structural normal force N acts to the right, the internal shear
members. force V acts downward, and the moment M acts
Draw the shear and moment counter clockwise. In accordance with Newton’s
diagrams of structural members third law, an equal but opposite normal force,
Apply Method of Superposition shear force, and bending moment must act on
in drawing moment diagrams. the right-hand face of the member at the section.
Calculate the internal shear and Perhaps an easy way to remember this sign
moment of structural members convention is to isolate a small segment of the
Learning Activities member and note that positive normal force
Activities for Do the assignments and tends to elongate the segment, Fig. b; positive
this module problem sets shear tends to rotate the segment clockwise, Fig.
Take the quiz (Quiz1) c; and positive bending moment tends to bend
Graded Assessment the segment concave upward, so as to “hold
Evidence to Completed all the water,” Fig.d.
proceed assessment tasks in this
module
References
Printed National Structural Code of the
Sources Philippines, 5th ed. Association
of Structural Engineers of the
Philippines, Manila 2001 by
Association of Structural
Engineers of the Philippines
Structural Analysis, 4th Ed,
Prentice Hall 1999., N.J. By:
Hibbler, R.C.
Structural Analysis, By: Besavilla
Structural Analysis, By: Gillesania
Internal Loadings Developed in Structural
Members
Internal Loadings at a Specified Point
Shear and Moment Functions
Shear and Moment Diagrams for Beams
Shear and Moment Diagrams for a Frames
Moment Diagrams Constructed by the
Method of Superposition
Deflected Shapes
SHEAR AND MOMENT FUNCTIONS
SHEAR AND MOMENT DIAGRAMS FOR BEAMS
Example
Determine the shear and moment in the beam
shown in figure as a function of x.
MOMENT DIAGRAMS CONSTRUCTED BY THE
METHOD OF SUPERPOSITION
Most loading on beams in structural analysis will
be a combination of the loadings shown in the
figure below:
SHEAR AND MOMENT DIAGRAMS FOR FRAMES
Example
DEFLECTED CURVE
Example 1 Example 3
Determine the internal shear and moment acting The 40 kN force in the figure is supported by the
in the cantilever beam shown in the figure at floor panel DE, which in turn is simply supported at
sections passing through points C and D. 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.
Example 2
Determine the internal shear and moment acting
at a section passing through point C in the beam
shown in the figure.
Example 4
Draw the shear and moment diagrams for the
compound beam shown in the figure. Assume the
supports at A and C are rollers and B and D are
pin connections.
Example 5
Draw the shear
and moment
diagrams for the
frame shown.
Assume A, C and
D are pinned and
B is a fixed joint.
Example 6
Draw the moment
diagram for the
frame shown.
Assume A is pin, C
is a roller, and B is
a fixed joint.
Example 7
Draw the moment
diagrams for the
beam shown at the
top of the figure
below using the
method of superposition. Consider the beam to
be cantilevered from the support at B.
