Solid Mechanics
1. Shear force and bending moment
diagrams
Internal Forces in solids
Sign conventions
1
and Vz
2
The couple moment along the axis of the member is
given
M x = T = Torque
M y = M z = bending moment.
Shear forces are given a special symbol
Structural Axial, Shear
and Bending Moments
Positive Internal Forces Acting
on a Portal Frame
1
Recall from mechanics of materials that the internal forces P
(generic axial), V (shear) and M
(moment) represent resultants of
the stress distribution acting
Beams SFD and BMD
Shear and Moment Relationships
dV
w
dx
Slope of the shear diagram = - Value of applied loading
dM
V
dx
Slope of the moment curve = Shear Force
Both equations not applicable at the point of loading because
of discontinuity produced by the
Shear and Bending Moment
Diagrams
(Credit for many illustrations is given to McGraw Hill publishers and an array of
internet search results)
Parallel Reading
Chapter 5
Section 5.1
Section 5.2
Section 5.3
Section 5.4
Section 5.5
(Do Chapter 5 Reading Assig
Shear Force and Bending
Moment
Shear Force: is the algebraic sum of the
vertical forces acting to the left or right
of a cut section along the span of the
beam
Bending Moment: is the algebraic sum
of the moment of the forces to the left or
to the right
BEAM DESIGN FORMULAS
WITH SHEAR AND MOMENT
DIAGRAMS
2005 EDITION
ANSI/AF&PA NDS-2005
Approval Date: JANUARY 6, 2005
ASD/LRFD
N DS
NATIONAL DESIGN SPECIFICATION
FOR WOOD CONSTRUCTION
WITH COMMENTARY AND
SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION
Ameri
Mechanics of Materials
Chaper4
Shear Force and Bending Moment in Beams
HENAN UNIVERSITY OF SCIENCE & TECHNOLOGY
Edited by YANG MIN-xian
1
CHAPTER 4
Shear Force and Bending Moment in Beams
41 Concepts of planar bending and calculation sketch of the beam
42
How to find Bending Moment
Bending Moment 1.
CH28 p355
Bending moment is a torque applied to each side of the beam if
it was cut in two - anywhere along its length.
The hinge applies a clockwise (+) moment (torque) to the RHS,
and a counter-clockwise (-)
M = RA x
RA - P1
A
P1 (x - a1)
Shearing Force and
Bending Moment
- P1 )(a2 - a1)
hat point
Lecturer;
Dr. Dawood S. Atrushi
bending
le beam
a
<
x < a
+
b
V
=
RA - q (x - a)
M
=
RA x
- q (x - a)2 / 2
November 2014
Content
Beams
Type of beams, loadings, and
Beam Analysis
We require from buildings two kinds of
goodness: first, the doing their practical duty
well: then that they be graceful and pleasing
in doing it.
-John Ruskin
Beam
Structural member that carries a load that
is applied transverse to its leng
Chapter 5
The 1st chapter in 2nd term
Introduction :
In this chapter we care for the analysis and the
design of beams ,structural members supporting
loads applied at different points ,In most cases
,the loads are perpendicular to the axis of the
beam ,whe
Some Guidelines for Constructing Shear Force and Bending Moment Diagrams
SIGN CONVENTIONS
+V
-V
+M
+M
+V
-M
-M
-V
BOUNDARY CONDITIONS
B
A
Ax
Ay
Pinned LEFT End:
Reaction force, Ax is unknown.
Reaction force, Ay is unknown.
V (shear force) = Ay (reaction f