engineering

MULTI-AXIS LOADING MECH 3315 Mechanics Lab

Purpose In this experiment, an offset load is applied to a cantilevered pipe to produce multiple stresses along the length of the tube and near the support. The superposition of these stresses results in a strain that is measured near the support where the maximum stresses and strains occur. These strains can then be compared to those predicted using principal stresses and plane stress assumptions.

Procedure 1. Mount the support bracket and main pipe to a table with two C-clamps. Be sure to allow space for mounting the smaller

torsion bar horizontally.

2. Attach the horizontal bar to the end of the pipe and use the thumb screws to adjust the distance between screws to roughly 12 inches. Place an unloaded weight hanger against the outer thumb screw. This is your unloaded configuration.

3. Measure the dimensions of the pipe and load bar. Be sure to get inside and outside diameters as well as estimated distances from the hanger to the center of the pipe and center of the pipe (where the two pipes cross) to the center of the strain gages.

4. Connect the three strain gages on the top of the beam to a NI-9237 DAQ using three quarter bridge completion blocks.

5. Write LabVIEW code to collect strain from each gage as different loads are applied. Be sure to run a calibration of each gage with the hanger attached but with no weights. The gage information is taped to the pipe.

6. Add weights using 2 lbf increments to the hanger until you reach 20 lbf, recording the strains at each load. Reverse the process by removing weights and repeat until you are satisfied with the number of measurements.

7. Return the experiment to its initial state and put away all equipment used.

Last updated: February 23, 2017 EAD 1

MULTI-AXIS LOADING MECH 3315 Mechanics Lab

Theory and analysis Further information on stresses and strains for combined loading came be found in Ugural & Fenster, Advanced Mechanics of Materials and Applied Elasticity.

The base of the pipe experiences three loadings: bending, torsion, and shearing. Since the shearing component is zero at the top and bottom of the beam only simple bending

σx = Mc

I , (1)

with bending moment M, distance to neutral axis c, and area moment of inertia I, and torsion shear stress

τ = Tc

J , (2)

with torque T and polar moment of inertia J, remain.

Plane strains are calculated using a generalized Hooke’s law approach as

�x = 1

E [σx − ν (σy + σz)] (3)

�y = 1

E [σy − ν (σx + σz)] , (4)

with modulus E and Poisson ratio ν.

These can be used to find the principal stresses for plane stress

σ1,2 = σx + σy

2 ±

√( σx − σy

2

)2 + τ2xy (5)

and the principal strains

�1,2 = �x + �y

2 ±

√( �x − �y

2

)2 + (γxy

2

)2 , (6)

where γxy = τxy G

with shear modulus G.

Report requirements Please see the handout on laboratory technical papers for a general discussion. All values should be reported with combined (bias + precision) uncertainty. Particular results for this lab must include:

• Plot/table - Comparison of measured principal stresses and strains with predicted stresses and strains as a function of the applied moment

Last updated: February 23, 2017 EAD 2