Finding the shear centre of a non-homogeneous cross section cross

In summary, to find the shear centre of a cross section with a ratio of Eb/Ep=30, the equivalent cross section must be found by increasing the length of the horizontal parts by a factor of 30. Then, using the axis of symmetry, the distance "eo" can be found by moving the force to the shear centre and calculating the moment. The equation for shearing stress is V*Q/I/b, where 2.15 is the distance between the horizontal forces. By expanding the cross section incorrectly, the calculated answer was 14.7cm, while expanding it correctly gave a result of 0.49cm. It is possible that the given answer in the textbook (0.408cm) is incorrect.
  • #1
Dell
590
0
for the following cross section
Capture.JPG

the ratio Eb/Ep=30

find the shear centre of the cross section
-------------------------------------------
first of all i need to find the equivalent cross section, which will be the same except that the horizontal parts will be of length n*L=30*1=30cm

since this cross section has an axis of symmetry, i know that the shear centre passes through that axis, now all i need to find is the distance "eo"

i know that i can move the force to the shear centre and the cross section must feel the same moment, i calculated the moment about a point that passes through the Vertical portion so that only the sums of the horizontal shearing stresses have an effect on the moment,

i know that Q1y is the 1st area moment of each of the horizantal portions,

Q1y=(0.15*s)*1.075 =0.16125*s

I=10.6cm^4

shearing stress=[tex]\int[/tex][tex]\int[/tex](V*Q/I/b)da*2.15 where 2.15 is the distance between the horizontal forces

V*e=[tex]\int[/tex][tex]\int[/tex](V*Q/I/b)da*2.15

e=2.15/(I*0.15)*[tex]\int[/tex]dt[tex]\int[/tex]Qds

e=[2.15/(I*0.15)]*0.15*[tex]\int[/tex](0.16125*s)ds -->from 0 to 30



[2.15/(10.6*0.15)]*0.15*0.16125*302/2=14.7cm

the correct answer is somehow meant to be 0.408cm, can anyone see where i have gone wrong??
 
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  • #2
your line: "shearing stress=LaTeX Code: \\int LaTeX Code: \\int (V*Q/I/b)da*2.15 where 2.15 is the distance between the horizontal forces"

comment: I'm not sure what all those integral signs are doing. I thought shearing stress was just V*Q/I/b. (That is, the result of integration). OK, so you multiply by area to get force, and then by 2.15 to obtain moment. So should your "shearing stress" read as "moment"?
 
  • #3
o yes, that's correct, meant to be moment, but it still won't change the answer,

im beginning to think that the way i expanded the cross section was incorrect, i just made the 2 horizontals 30 times longer ( to the right) maybe i was meant to expand them to both sides, 14.5 to each side,

doing this would still not give me a correct answer, but much closer,
by doing this i get 0.49cm

is it possible that the answer i was given in the textbook (0.408) is incorrect,
could someone please check this for me
 

1. What is the shear centre of a non-homogeneous cross section cross?

The shear centre of a non-homogeneous cross section cross is a point where the application of a shear force does not cause any twisting or rotation of the cross section. In other words, it is the point at which the shear force can be applied without causing any bending.

2. Why is it important to find the shear centre of a non-homogeneous cross section cross?

Finding the shear centre is important because it allows us to accurately predict the behavior of the cross section under shear forces. This information is crucial in structural design and analysis, as it ensures the safety and stability of the structure.

3. How is the shear centre of a non-homogeneous cross section cross calculated?

The shear centre of a non-homogeneous cross section cross is typically calculated using mathematical equations and formulas based on the geometry and material properties of the cross section. Computer software and numerical methods may also be used for more complex cross sections.

4. What factors affect the location of the shear centre in a non-homogeneous cross section cross?

The location of the shear centre in a non-homogeneous cross section cross is affected by several factors, including the shape, material properties, and loading conditions of the cross section. Any asymmetry or variation in the cross section can also impact the location of the shear centre.

5. Can the shear centre of a non-homogeneous cross section cross change under different loading conditions?

Yes, the shear centre of a non-homogeneous cross section cross can change under different loading conditions. This is because the distribution of shear forces can vary, causing the point of zero twisting to shift. It is important to consider all potential loading scenarios when determining the shear centre of a non-homogeneous cross section cross.

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