Transcript Title

SM1-02: Statics 1: Internal forces in bars
INTERNAL FORCES
IN BARS
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SM1-02: Statics 1: Internal forces in bars
L
Definitions
Bar axis
•Bar – a body for which L»H,B
•Bar axis - locus of gravitational
centres of bar sections cutting its
surface
•Prismatic bar – when generator of
bar surface is parallel to the bar
axis
H
B
•Straight bar – when bar axis is a
straight line
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SM1-02: Statics 1: Internal forces in bars
Assumptions
•Bar axis represents the whole body
and loading is applied not to the
bar surface but the bar axis
P
M
.
•Set of bar and loading will be
considered as the plane one if
forces acts in plane of the bar.
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q
M
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SM1-02: Statics 1: Internal forces in bars
Agreements
n
•Reduction centre O is located on
the bar axis by vector r0
O
•Internal forces are determined on
the planes perpendicular to the
bar axis (vector n is parallel to the
axis)
•Vector n is an outward normal
vector
n
z
r0
x
y
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SM1-02: Statics 1: Internal forces in bars
In 3D vectors of internal forces resultants have three components each
Swz
Sw
z
Sny
x
y
Mwz
Swx
Sw{ Swx , Swy , Swz }
Mwy
Mw
Mwx
Mw{ Mwx , Mwy , Mwz }
Components of internal forces resultants
Swx , Swy , Swz and Mwx , Mwy , Mwz
are called cross-sectional forces
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SM1-02: Statics 1: Internal forces in bars
Sw = Sw(rO , n)
Mw = Mw(rO , n)
Resultants of internal forces are vector
functions of two vectors ro and n
Vector n is known if we
know the shape of bar
axis
Thus, resultants of internal forces
for known bar structure are function
of only one vector r0
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n
Sw = Sw(rO)
Mw = Mw(rO)
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SM1-02: Statics 1: Internal forces in bars
In 2D number of cross-sectional forces
is reduced, because loading and bars
axes are in the same plane (x, z):
M
.
M
q
Sw{ Sx , 0, Sz }
Sz
Mw{ 0, My , 0 }
We will use following notations and
names for these components:
Sx=N - axial forces
Sz=Q - shear force
z
Sx
My
x
y
My = M - bending moment
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SM1-02: Statics 1: Internal forces in bars
Special cases of internal forces reductions are
called:
N
TENSION – when internal forces reduce to the
sum vector only, which is parallel to the bar axis
SHEAR – when internal forces reduce to the sum
vector only, which is perpendicular to the bar
axis
BENDING – when internal forces reduce to the
moment vector only, which is perpendicular to
the bar axis
TORSION – when internal forces reduce to the
moment vector only, which is parallel to the bar
axis
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M
Ms
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SM1-02: Statics 1: Internal forces in bars
stop
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