# Maximum theoretical and experimental stress in T-beam.

1. Nov 25, 2013

### SherlockOhms

1. The problem statement, all variables and given/known data
1. Take dimensions of the beam (B, D, web and flange thickness, L) – T- cross section
2. Take the beam span geometry and material properties from the instrument
3. Ensure the beam and load cell are properly aligned and apply a positive (downward) preload to the beam of 100N. Zero the load cell using the control.
4. Take zero readings for all 9 gauges.
5. Increase load to 100N and take note of the readings. Repeat procedure in 100N increments to 500N
7. Convert the load to a bending moment
8. Plot a graph of strain against bending moment for all 9 gauges (on one graph)
9. Calculate the average strains from the pairs of gauges, where applicable
10. Plot a graph of strain against gauge position using T beam cross section
11. Locate experimental neutral axis and compare with theoretical
12. Calculate and compare maximum experimental and theoretical stress

2. Relevant equations
$\sigma = \frac{My}{I}$

3. The attempt at a solution
So, this was an experiment in which there were strain gauges set up along a T-beam and we were asked to measure the strain at various different points whilst applying different loads. Could someone tell me how I go about calculating the maximum theoretical stress? Is it by the equation: $$\sigma = \frac{My}{I}$$ where M is the moment about the neutral axis, y is the displacement (in this case it'll be the maximum distance allowable from the neutral axis) and I is the second moment of area? I have absolutely no clue how to calculate the max experimental stress. Any hints/tips?
Also, I'll attach a picture of the T-beam (a miniature version with the dimensions).
The flange and web width are 6.4.
The length is shown in the diagram on the left.

#### Attached Files:

• ###### Beam Dimension (BEAM EXP).jpg
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2. Nov 25, 2013

### rock.freak667

From your graph you would get the maximum strain which would correspond to the maximum stressed area.

For the theoretical max stress, you would need to calculate I for the T section and find the location of the neutral axis (remember how to find centroids?). From the loading conditions, you would also need to find the maximum bending moment and where it occurs.

3. Nov 26, 2013

### SherlockOhms

So, is your first part for the max experimental stress? Like, I find the max stressed area and then divide the maximum load by this? I'm not sure if I follow.

Well, the loads act at along the beams length, 350 mm from the ends. So, the bending moment will be -W/2 x 0.35? I've already calculated $y_{theoretical}$ and $I$ for the T-section. So, would I just sub in, the maximum distance from $y_{theoretical}$, $I$ and -W/2 x .35 into my equation for bending stress?