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Schemi Statici
Structural Analysis of Simple Beams

Free Solution with Dynamic Diagrams: Displacement, Moment, Shear
Cantilever Beams
Cantilever Beam
with Uniformly Distributed Load
Cantilever Beam
Uniformly Distributed Load
Moment on beam end
Concentrated Load on beam end
Cantilever Beam
with Two Uniformly Distributed Loads
and Two Concentrated Loads
Simply Supported Beams
Beam extending on two supports
with Uniformly Distributed Load
Beam extending on two supports
with Two Uniformly Distributed Loads
and a Concentrated Load
Beam extending on two supports
with three Uniformly
Distributed Loads
and Two Concentrated Loads
Beam extending on two supports
with Uniformly Distributed Load
and Two Moments on beam ends
Beam extending on two supports
with Two Uniformly Distributed Loads
Concentrated Load
and Moments
Overhanging Beams
Overhanging Beam
with Two Uniformly Distributed Loads
and One Load Applied at End
Overhanging Beam
with Uniformly Distributed Loads,
Concentrated Loads
and One Moment Applied at End
Double Overhanging Beam
with Uniformly Distributed Loads,
and Loads Applied at Ends
Double Overhanging Beam
with Uniformly Distributed Loads,
Concentrated Loads
and Moments Applied at Ends
Propped Cantilever Beams
Propped Cantilever Beam
with Uniformly Distributed Load
Propped Cantilever Beam
with Two Uniformly Distributed Loads
and One Concentrated Load
Propped Cantilever Beam
with
Internal Hinge
,
Two Uniformly Distributed Loads
and one Load Applied on hinge
Propped Cantilever Beam
with Uniformly Distributed Loads
and Two Concentrated Loads
Propped Cantilever Beam
with Uniformly Distributed Load
and One Moment on Beam End
Propped Cantilever Beam
with Two Uniformly Distributed Loads
One Concentrated Load
and Moments
Propped CantileverOverhang Beams
Propped CantileverOverhang Beam
with Two Uniformly Distributed Loads
and One Load Applied at End
Propped CantileverOverhang Beam
with Uniformly Distributed Loads
Concentrated Loads
and One Moment Applied at End
Propped CantileverOverhang Beam
with
Internal Hinge
,
Uniformly Distributed Loads
and One Moment Applied at End
Fixed Beams
Fixed Beam
with Uniformly Distributed Load
Fixed Beam
with Two Uniformly Distributed Loads
and One Concentrated Load
Fixed Beam
with Uniformly Distributed Loads
and Two Concentrated Loads
Fixed Beam
with Two Uniformly Distributed Loads
One Concentrated Load
and One Concentrated Moment
1
2
1'000,00 daN/m
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Italiano
English
Material
MATERIAL
Young's Modulus
(
E
) the same for all the beams.
Therefore this value will affect only the deformed shape;
while it not have influence for the diagrams of the Moment
of the Shear, and Axial Force
It's always necessary to press "UPDATE GRAPHICS AND TABLES", because the changes take effect
E
:
daN/cm
2
Moment of inertia
MOMENT of INERTIA
Area Moment of Inertia
(
J
) the same for all the beams.
Therefore this value will affect only the deformed shape;
while it not have influence for the diagrams of the Moment
of the Shear, and Axial Force
It's always necessary to press "UPDATE GRAPHICS AND TABLES", because the changes take effect
Example of calculation:
J
_{rectangle}
= B*H
^{3}
/12
J
_{circle }
= π*r
^{4}
/4
J
:
cm
4
Beam 1 ⇒ 2
BEAM
among the node
1
and the node
2
Length
(
L
) defined as the distance between the two nodes
It's always necessary to press "UPDATE GRAPHICS AND TABLES", because the changes take effect
L
:
cm
BEAM
among the node
1
and the node
2
Uniformly Distributed Load
(
q
)
applied in the orthogonal direction at the beam
It's always necessary to press "UPDATE GRAPHICS AND TABLES", because the changes take effect
q
:
daN/m
1
2
Displacement
Δ
vertical
=
+0
cm
(calculated at 0 cm from the node n° 1)
Displacement
Δ
vertical
=
0.2226
cm
(calculated at 20,0 cm from the node n° 1)
Displacement
Δ
vertical
=
0.8317
cm
(calculated at 40,0 cm from the node n° 1)
Displacement
Δ
vertical
=
1,746
cm
(calculated at 60,0 cm from the node n° 1)
Displacement
Δ
vertical
=
2,895
cm
(calculated at 80,0 cm from the node n° 1)
Displacement
Δ
vertical
=
4,216
cm
(calculated at 100 cm from the node n° 1)
Displacement
Δ
vertical
=
5,657
cm
(calculated at 120 cm from the node n° 1)
Displacement
Δ
vertical
=
7,175
cm
(calculated at 140 cm from the node n° 1)
Displacement
Δ
vertical
=
8,737
cm
(calculated at 160 cm from the node n° 1)
Displacement
Δ
vertical
=
10,32
cm
(calculated at 180 cm from the node n° 1)
The Maximum Shift
of all the structure
Δ
vertical
=
11,90
cm
(calculated at 200 cm from the node n° 1)
DISPLACEMENTS
Maximum Displacement of Structure
Δ
_{max}
=
11,905
cm
The Maximum Shift
of all the structure
Δ
_{ vertical }
=
11,905
cm
Δ
_{ horizontal }
=
0
cm

Δ
_{ vector }
=
11,905
cm
Calculated at
200,0
cm
from the node n°
1
to the node n°
2
Beam (1 ⇒ 2)
Δvert. =
11,905
cm
Δoriz. =
0
cm
Relative Maximum Shift of beam
among the nodes
1
⇒
2
Δ
_{ vertical }
=
11,905
cm
Δ
_{ horizontal }
=
0
cm

Δ
_{ vector }
=
11,905
cm
Calculated at
200,0
cm
from the node n°
1
to the node n°
2
1
2
Bending Moment
M
sd
=
1 620
daN*m
(calculated at 0.2 m from the node n° 1)
Bending Moment
M
sd
=
1 280
daN*m
(calculated at 0.4 m from the node n° 1)
Bending Moment
M
sd
=
980,0
daN*m
(calculated at 0.6 m from the node n° 1)
Bending Moment
M
sd
=
720,0
daN*m
(calculated at 0.8 m from the node n° 1)
Bending Moment
M
sd
=
500,0
daN*m
(calculated at 1,00 m from the node n° 1)
Bending Moment
M
sd
=
320,0
daN*m
(calculated at 1,20 m from the node n° 1)
Bending Moment
M
sd
=
180,0
daN*m
(calculated at 1,40 m from the node n° 1)
Bending Moment
M
sd
=
80,00
daN*m
(calculated at 1,60 m from the node n° 1)
Bending Moment
M
sd
=
20,00
daN*m
(calculated at 1,80 m from the node n° 1)
The Maximum Moment
of all the structure
M
sd
=
2 000
daN*m
(calculated at 0 m from the node n° 1)
The Minimum Moment
of all the structure
M
sd
=
0
daN*m
(calculated at 2,00 m from the node n° 1)
BENDING MOMENT
The Maximum Moment
M
_{sd}
=
2 000
daN*m
The Maximum Moment
of all the structure
M
_{sd}
=
2 000
daN*m
Calculated at
0
m
from the node n°
1
to the node n°
2
Beam (1 ⇒ 2)
M
sd (max)
=
2 000
daN*m
M
sd (min)
=
0
daN*m
Maximum and Minimum Relative Moments
of the beam among the nodes
1
⇒
2
M
_{sd maximum }
=
2 000
daN*m
Calculated at
0
m
from the node n°
1
to the node n°
2
M
_{sd minimum }
=
0
daN*m
Calculated at
2,000
m
from the node n°
1
to the node n°
2
1
2
Shear
V
sd
=
1 800
daN
(calculated at 20,0 cm from the node n° 1)
Shear
V
sd
=
1 600
daN
(calculated at 40,0 cm from the node n° 1)
Shear
V
sd
=
1 400
daN
(calculated at 60,0 cm from the node n° 1)
Shear
V
sd
=
1 200
daN
(calculated at 80,0 cm from the node n° 1)
Shear
V
sd
=
1 000,0
daN
(calculated at 100 cm from the node n° 1)
Shear
V
sd
=
800,0
daN
(calculated at 120 cm from the node n° 1)
Shear
V
sd
=
600,0
daN
(calculated at 140 cm from the node n° 1)
Shear
V
sd
=
400,0
daN
(calculated at 160 cm from the node n° 1)
Shear
V
sd
=
200,0
daN
(calculated at 180 cm from the node n° 1)
The Minimum Shear
of all the structure
V
sd
=
2 000
daN
(calculated at 0 cm from the node n° 1)
The Maximum Shear
of all the structure
V
sd
=
0
daN
(calculated at 200 cm from the node n° 1)
SHEAR
The Maximum Shear
V
_{sd}
=
2 000
daN
The Maximum Shear
of all the structure
V
_{sd}
=
2 000
daN
Calculated at
0
cm
from the node n°
1
to the node n°
2
Beam (1 ⇒ 2)
V
sd (max)
=
0
daN
V
sd (min)
=
2 000
daN
Maximum and Minimum Relative Shears
of the beam among the nodes
1
⇒
2
V
_{sd maximum }
=
0
daN
Calculated at
200,0
cm
from the node n°
1
to the node n°
2
V
_{sd minimum }
=
2 000
daN
Calculated at
0
cm
from the node n°
1
to the node n°
2
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