Calculating Shear Force for an Elastomeric Bearing Pad

[donniemateno]

Gents and Ladies

I have a question I have been given to work out shear force for.

The question is an elastomeric bearing pad is subjected to a shear force V

the top plate is found to have displaced by d = 12mm

dimensions of the top pad are a = 150mm by b = 200mm, the thickness (d) is 120mm. the modulus of rigidity G is 2 MPA

I have found a formula which is shear stress is t=Gy

y = d/h so 12 / 120 = 0.1

shear stress 2000 x 0.1 = 200 Kn

i fear i have done something wrong because i haven't used the dimensions of the plate. I have a formula which gives the average stress which is stress = v / ab but if i rearrange i get v = ab / stress

 

[donniemateno]

any help at all ? please :)?

 

[Chestermiller]

You calculated the shear strain correctly. The shear stress is equal to the shear strain times the shear modulus G. The shear stress should be in units of MPa. In your case the shear stress is 0.2 MPa. The shear force is equal to the shear stress times the area over which the stress is applied. What is the area of the pad? You do know that 1 Pa = 1 N/m², and that 1 MPa = 1000000 Pa, correct?

 

[donniemateno]

so it should by 0.2 x 0.1? for shear stress? = 0.2 * area ( 150 * 200) = 30000 N so would it be 30Kn?

 

[Chestermiller]

Please be more careful with your arithmetic.

Shear stress = 2 x 0.1 = 0.2 MPa

What is the area in square meters?

What is the stress times the area in consistent units?

 

[donniemateno]

Would my 150 and 200 mm become 1.5 and 2? making 3 square meters

 

[Chestermiller]

No. Do you know the definition of a millimeter (mm)?

 

[donniemateno]

yes 1000mm to a meter 10mm to a cm

so my 150 mm and 200mm should be .15 * .2? this times by 0.2 would give me 0.006

 

[Chestermiller]

Yes. Bu what are the units?

 

[donniemateno]

Would this be 6 N? Seems very low. I thought the answer would be more like 6 Kn based on an example I have worked out gpa

 

[Chestermiller]

No. We already said that 1MPa = 1000000 N/m². So if you apply the units correctly, you get 6000 N = 6 kN.

 

[donniemateno]

Ive been asked to express answer is n not kn. Thank yu for your help :) sorry I am slow