Structural Analysis of Simple Beams

  -  

Free Solution with Dynamic Diagrams: Displacement, Moment, Shear

12 -1'000,00 daN/m
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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:
Jrectangle = B*H3/12
Jcircle      = π*r4/4
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
12 DisplacementΔ vertical      = +0 cm(calculated at 0 cm from the node n° 1) DisplacementΔ vertical      =  -0.2226 cm(calculated at 20,0 cm from the node n° 1) DisplacementΔ vertical      =  -0.8317 cm(calculated at 40,0 cm from the node n° 1) DisplacementΔ vertical      =  -1,746 cm(calculated at 60,0 cm from the node n° 1) DisplacementΔ vertical      =  -2,895 cm(calculated at 80,0 cm from the node n° 1) DisplacementΔ vertical      =  -4,216 cm(calculated at 100 cm from the node n° 1) DisplacementΔ vertical      =  -5,657 cm(calculated at 120 cm from the node n° 1) DisplacementΔ vertical      =  -7,175 cm(calculated at 140 cm from the node n° 1) DisplacementΔ vertical      =  -8,737 cm(calculated at 160 cm from the node n° 1) DisplacementΔ vertical      =  -10,32 cm(calculated at 180 cm from the node n° 1) The Maximum Shiftof all the structureΔ vertical      =  -11,90 cm(calculated at 200 cm from the node n° 1)
DISPLACEMENTS
Maximum Displacement of Structure
Δmax = 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
12 Bending MomentMsd = 1 620 daN*m(calculated at 0.2 m from the node n° 1) Bending MomentMsd = 1 280 daN*m(calculated at 0.4 m from the node n° 1) Bending MomentMsd = 980,0 daN*m(calculated at 0.6 m from the node n° 1) Bending MomentMsd = 720,0 daN*m(calculated at 0.8 m from the node n° 1) Bending MomentMsd = 500,0 daN*m(calculated at 1,00 m from the node n° 1) Bending MomentMsd = 320,0 daN*m(calculated at 1,20 m from the node n° 1) Bending MomentMsd = 180,0 daN*m(calculated at 1,40 m from the node n° 1) Bending MomentMsd = 80,00 daN*m(calculated at 1,60 m from the node n° 1) Bending MomentMsd = 20,00 daN*m(calculated at 1,80 m from the node n° 1) The Maximum Momentof all the structureMsd = 2 000 daN*m(calculated at 0 m from the node n° 1) The Minimum Momentof all the structureMsd = 0 daN*m(calculated at 2,00 m from the node n° 1)
BENDING MOMENT
The Maximum Moment
Msd = 2 000 daN*m
The Maximum Moment
of all the structure

Msd = 2 000 daN*m

Calculated at 0 m
from the node n° 1 to the node n° 2
Beam (1 ⇒ 2)
Msd (max) =
2 000
  daN*m
 
Msd (min)  =
0
  daN*m
Maximum and Minimum Relative Moments
of the beam among the nodes 1 ⇒ 2

Msd maximum  = 2 000 daN*m
Calculated at 0 m
from the node n° 1 to the node n° 2

Msd minimum   = 0 daN*m
Calculated at 2,000 m
from the node n° 1 to the node n° 2

12 ShearVsd = -1 800 daN(calculated at 20,0 cm from the node n° 1) ShearVsd = -1 600 daN(calculated at 40,0 cm from the node n° 1) ShearVsd = -1 400 daN(calculated at 60,0 cm from the node n° 1) ShearVsd = -1 200 daN(calculated at 80,0 cm from the node n° 1) ShearVsd = -1 000,0 daN(calculated at 100 cm from the node n° 1) ShearVsd = -800,0 daN(calculated at 120 cm from the node n° 1) ShearVsd = -600,0 daN(calculated at 140 cm from the node n° 1) ShearVsd = -400,0 daN(calculated at 160 cm from the node n° 1) ShearVsd = -200,0 daN(calculated at 180 cm from the node n° 1) The Minimum Shearof all the structureVsd = -2 000 daN(calculated at 0 cm from the node n° 1) The Maximum Shearof all the structureVsd = 0 daN(calculated at 200 cm from the node n° 1)
SHEAR
The Maximum Shear
Vsd = -2 000 daN
The Maximum Shear
of all the structure

Vsd = -2 000 daN

Calculated at 0 cm
from the node n° 1 to the node n° 2
Beam (1 ⇒ 2)
Vsd (max) =
0
  daN
 
Vsd (min)  =
-2 000
  daN
Maximum and Minimum Relative Shears
of the beam among the nodes 1 ⇒ 2

Vsd maximum  = 0 daN
Calculated at 200,0 cm
from the node n° 1 to the node n° 2

Vsd minimum   = -2 000 daN
Calculated at 0 cm
from the node n° 1 to the node n° 2



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