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ESTIMATE THE EFFECTIVE BREADTH OF

PLATES OF SIMPLY SUPPORTED BEAMS
• CLEINER MARIN
• JORGE ALCIVAR
• ANDRES ORTEGA

AGENDA
OBJETIVE
o Objetive Check Schade’s method to estimate the
o Introduction effective breadth of plates of simply
o SHADE’S Method supported beams .

o Experimental method
o Results
o Conclusions and
recommendations.

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INTRODUCTION SHADE’S METHOD

for this practice we need to check the
Schade’s formula for the effective breath.
To get the objective the strain was
measured in 3 different position changing
the applied force ant the length of the
Strain in x direction
beam, using the expression in the Schade
paper was found the effective breath
experimentally. To compare the theory
was used graph “ʎ/b vs cL/B”.
Quantity of plate or flange breadth that Will
support the maximun stress

EXPERIMENTAL METHOD
In concetrated load the variable cL
represent the distance between point
Variables in this practice
where de bending moment is 0 .
Applied force
Lenght between supports
Unitary deformation

Unitary Stress Maximum Effective

Deformation Distribution Stress Breadth
(Integrate)

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ESTIMATED VALUE BEFORE PRACTICE

• FOR THE BENDING MOMENT DISTRIBUTION:
RESULTS
𝑀(𝑥)=𝐹𝛿(𝑥−𝑙/2)*𝐸[𝑥−𝑙/2]−𝐹𝑥/2 Reading of Strain and deformations in the strain
gages for diferents applied forces
• BC: 𝑀(0)=0; 𝑀(𝐿)=0; 𝑀(𝐿/2)=𝑃(𝑙/2)/2 when L=132 [cm]
• ASSUMING P=75 KG AND L=1,32 M
• 𝑀(𝐿/2)=2850 [KG*CM]
• THE FIRTS MOMENT OF ÁREA:
𝑄=81.25 [𝑐𝑚^3]
• THE MAXIMUM EFFORT EXPECTED: when L=158cm [cm]
strain 10^-6 stress kg/cm2
𝜎𝑚𝑎𝑥= 35,07 [𝑘𝑔/𝑐𝑚^2] ch 3 medio Ch 5 centro ch7 extremo ch 3 medio Ch 5 centro
ch7 área bajo la
stress maxi λ/b
extremo curva
• THE EXPECTED DEFORMATION: -0,27
8,71
-0,20
9,85
-0,28
9,10
-0,20
6,28
-0,14
7,10
-0,20
6,56
-1,12
48,11
-0,14
7,10
1,14
0,97 Comparation of result whit error
𝜀𝑥=𝜎𝑚𝑎𝑥/𝐸= 5,57E-5 18,29
31,76
21,05
37,48
19,41
34,29
13,19
22,90
15,18
27,03
14,00
24,72
102,54
181,68
15,18
27,03
0,97
0,96
between 6-7%:
15,55 18,95 17,19 11,21 13,67 12,40 91,32 13,67 0,95 We can see that effetivity increase
5,94
-1,91
7,35
-1,56
6,67
-1,64
4,28
-1,38
5,30
-1,12
4,81
-1,18
35,35
-8,22
5,30
-1,12
0,95
1,05 when L=l58cm

Tendence line of efective breadth with applied

forces for L=152cm and L=132cm
CONCLUSIONS AND
RECOMMENDATIONS
• the experimental data are significantly closer to the formulation used by schades
The graph shown the comparation
between of the teoretical and
• no matter the magnitude of load that is subject to the beam, if it increases, the
experimental values of the
distribution of stress and maximum stress also increases, but the relationship
effective breadth , in which have
between them is maintained and is equal to the effective breadth.
low estandar desviation
• put extensometers in the two parts of the wing of the beam, to check if the results
are symmetrical, and we would get another way to check what schades says

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