DMV 4343 JAN ~ JUN `07 DEPARTMENT MANUFACTURING / PRODUCT DESIGN / MOULD / TOOL AND DIE SEMESTER 4 / 6 COURSE MECHANICS OF MATERIALS DURATION 8 hrs COURSE CODE DMV 4343 / DMV 5343 REF. NO. VTO’S NAME MISS AFZAN BINTI ROZALI MR RIDHWAN BIN RAMELI PAGE 18 TOPIC SHEAR FORCE AND BENDING MOMENT SUB TOPIC 4.1 Types of Beams and Loadings 4.2 Shear Force and Bending Moment Distribution 4.3 Relation between Distributed Load, Shear Force and Bending Moment 4.4 Shear Force and Bending Moment Diagrams Chapter 4 SHEAR FORCE AND BENDING MOMENT p0 INFORMATION SHEET
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DMV 4343JAN ~ JUN `07
DEPARTMENT MANUFACTURING / PRODUCT DESIGN / MOULD / TOOL AND DIE
SEMESTER 4 / 6
COURSE MECHANICS OF MATERIALS DURATION 8 hrsCOURSE CODE DMV 4343 / DMV 5343 REF. NO.VTO’S NAME MISS AFZAN BINTI ROZALI
MR RIDHWAN BIN RAMELIPAGE 18
TOPICSHEAR FORCE AND BENDING MOMENT
SUB TOPIC4.1 Types of Beams and Loadings4.2 Shear Force and Bending Moment Distribution 4.3 Relation between Distributed Load, Shear Force and Bending Moment4.4 Shear Force and Bending Moment Diagrams
Chapter 4 SHEAR FORCE AND BENDING MOMENT p0
INFORMATION SHEET
REF NO. :PAGE : 18
DMV 4343JAN ~ JUN `07
Chapter 4 SHEAR FORCE AND BENDING MOMENT p1
DMV 4343JAN ~ JUN `07
4.0 SHEAR FORCE AND BENDING MOMENT
Introduction
In previous chapter we have discussed the behavior of slender members subjected to axial
loading and to torsional loading. Now we turn our attention to the problem of determining the
stress distribution in, and the deflection of, beam.
A beam is a structural member that is designed to support transverse loads, that is, loads
that act perpendicular to the longitudinal axis of the beam. A beam resists applied loads by a
combination of internal transverse shear force and bending moment.
4.1 Types of Beams and Loadings
Beams
There are two classifications of beams:
Beams can be classified according to their cross-sectional shapes. For example, an I
beam and a T beam have cross sections geometrically formed like the letters I and T.
Beams of steel, aluminum, and wood are manufactured in standard sizes; their dimensions
and properties are listed in engineering handbooks. Tables B.2 through B.6 (App. B) present
several common cases of steel sections. These include wide-flange shapes (W beams),
(a) (b) (c)
FIGURE 4.1 Types of beams (a) I-shape, (b) L-shape, and (c) C-shape
I shapes (also called S beams), C shapes (also referred to as channels), and L shapes, or
angle sections. Note that the web is a thin vertical part of a beam. Thin horizontal parts of
the beam are termed flanges. Interestingly, the cross section of a beam is described as
doubly symmetric, singly symmetric, or asymmetric in accordance with whether it has two,
one, or no axis of symmetry.
Chapter 4 SHEAR FORCE AND BENDING MOMENT p2
web
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Beams can also be classified according to the way they are supported.
Lets first describe some common types of support.
Types of common support
Roller Support—prevents displacement in the transverse (i.e., y) direction, but permits
z-rotation and displacement in the axial direction; the reaction is a force in the +y or —y
direction. The support at end A in Figure 4.2a is a roller support.
Pin Support—prevents displacement in the axial direction and in the transverse
direction, but permits z-rotation; the reaction is a force with both axial and transverse
components. The support at end B in Figure 4.2a is a pin support.
Cantilever Support (or Fixed End)—prevents displacement in the axial direction and in
the transverse direction, and also prevents z-rotation; the reaction consists of a force
with both axial and transverse components, plus a couple. The support at end C in
Figure 4.2c is a cantilever support.
The types of support are summarized in following Table 4.1.
Chapter 4 SHEAR FORCE AND BENDING MOMENT p3
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TABLE 4-1 Reactions for types of connection
Chapter 4 SHEAR FORCE AND BENDING MOMENT p4
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Beams are normally classified by the manner in which they are supported.
(a) Simply Supported Beam—a beam with a pin support at one end and a roller support
at the other end. The beam in Figure 4.2a is a simply supported beam. Simply supported
beams are statically determinate.
(b) Fixed end (Propped) Cantilever Beam—a beam with a cantilever support (i.e., fixed
end) at one end and a roller at the other end. The beam in Figure 4.2b is a cantilever
beam. Propped cantilever beams are statically indeterminate.
(c) Cantilever Beam—a beam with a cantilever support (i.e., fixed end) at one end and
free at the other end. The beam in Figure 4.2c is a cantilever beam. Cantilever beams
are statically determinate.
(d) Fixed, simply supported beam –The beam in Figure 4.2d.
(e) Overhanging Beam—a beam that extends beyond the support at one end (or at both
ends). The beam in Figure 4.2e would be an overhanging beam if the roller support at
end A were to be moved to the right, leaving a part of the beam to the left of the roller as
an overhang.
(f) Continuous Beam—a beam with a pin support at one end, a roller support
at the other end, and one or more intermediate roller supports. The beam in Figure
4.2f is a continuous beam. Continuous beams are statically indeterminate.