Experiment: S1 – Bending Stresses in a T-Beam
Aims: To gain practical experience of strain measurement using strain gauges, to compare experimentally determined bending stresses with those predicted from Engineer’s Theory of Bending.
Learning Outcomes:
The evaluation of stresses and forces from experimental measurements of strain.
The determination of the position of the neutral axis of bending from experimentally determined bending stresses. The prediction of bending stresses from Engineer’s Theory of Bending.
Apparatus: Bench mounted loading frame with T-Beam
Procedure: The applied load was set to zero for each of the strain gauges 1-9 on the T-Beam. The applied load was increased on steps of 100N to a maximum load of 500N. At each load increment, strain measurements were taken induced from gauges 1-9. The results were attached at the worksheet. The applied load was decreased on steps of 100N until a zero load indicated. At each load reduction, strain measurements were taken induced from gauges 1-9. The results were attached at the worksheet. For each strain gauge, average strain gauge reading from 0-500N increment was evaluated. Graphs of load versus average strain for each gauge was plotted to check their linearity. There were comments on the results. The experimental bending stresses at each gauge for each load increment were evaluated using the formula ϭ= Es and graphs of bending stress versus gauge position were plotted and used to determine the position of the neutral axis of the section.
For a load of 400N only, the applied bending moment was evaluated. Using the equation
M/I = ϭ/y the theoretical bending stresses at each gauge position were determined and graphs of were plotted.
Figure1: T-Beam Loading and Cross-Section
Relevant Theory: E= ϭ/s
Where s = Strain
Ϭ = Stress
E = Young’s Modulus for the material
M/I = ϭ/y
Where
M = bending moment
Ϭ = stress
I = second moment of area of the section
y = distance from the neutral axis
For calculations, E=80GPa and I=60x103 mm4
Load (N)
Strain Gauge Readings (x10-6)
Load (N)
Strain Gauge Readings (x10-6)
Load (N)
Strain Gauge Readings (x10-6)
Member stress calculations
Load (N)
Strain Gauge Readings (x10-6)
Load (N)
Strain Gauge Readings (x10-6)
Load (N)
Strain Gauge Readings (x10-6)
is the experimental bending stresses (x10-3)
Using the load of 400N only
R=V (shear force) 200N
Maximum Moment (M) = the shear force area = 200N*350mm
=70000N/mm2
Using the formula: M/I = ϭ/y
ϭ = My/I and y =83.5/2 = 41.75
For gauge 1: y = 41.75
ϭ = 70000*41.75/60x103 = 47.71N/mm2
For gauge 2 and 3: y = 41.75-8=33.75
ϭ = 70000*33.75/60x103 = 39.375N/mm2
For gauge 4 and 5: y = 41.75-23=18.75
ϭ = 70000*18.75/60x103 = 21.875N/mm2
For gauge 6 and 7: y = 41.75-32=9.75
ϭ = 70000*9.75/60x103 = 11.375N/mm2
For gauge 8 and 9: y = 41.75-38.5=3.25
ϭ = 70000*3.25/60x103 = 3.792N/mm2
Work cited
Bolton, William. Mechanical Science. Malden, MA: Blackwell Publishers, 2005. Print.
