Maximum Deflection of Brass Beam: Troubleshooting Homework Solution

[Jonski]

Homework Statement

I am trying to find the maximum deflection in a brass beam, however after taking a physical reading the theoretical answer I get is quite off and I am wondering what I am doing wrong.

Homework Equations

They tell us the max deflection is( Load*Length^3)/(48*E*Second Moment of Area)
They also give us that E = 105GPA for brass

The Attempt at a Solution

The mass was 100g so load = 0.98N
Distance is 0.4 m
The problem I have is finding the correct moment of area as I think this is were I am getting it wrong. I have seen that for a rectangle it would be b*h^3/12
Then I = 0.4*0.00318^/12 = 1.07e-9 m^4
Putting this all together I get 11.63e-6m = 0.0116mm
The physical answer I got was 0.29mm.
Any ideas on what I am getting wrong

 

[SteamKing]

Homework Statement

I am trying to find the maximum deflection in a brass beam, however after taking a physical reading the theoretical answer I get is quite off and I am wondering what I am doing wrong.

Homework Equations

They tell us the max deflection is( Load*Length^3)/(48*E*Second Moment of Area)
They also give us that E = 105GPA for brass

The Attempt at a Solution

The mass was 100g so load = 0.98N
Distance is 0.4 m
The problem I have is finding the correct moment of area as I think this is were I am getting it wrong. I have seen that for a rectangle it would be b*h^3/12
Then I = 0.4*0.00318^/12 = 1.07e-9 m^4
Putting this all together I get 11.63e-6m = 0.0116mm
The physical answer I got was 0.29mm.
Any ideas on what I am getting wrong

Well, you provide some data, but not all which is necessary to analyze this problem.

How was the beam supported?
What were the dimensions of the beam (LxBxD)?
How was the cross section oriented with respect to the load?

Your inertia calculation suggests this beam was 40 cm wide and 3.18 mm thick. That's a very odd set of dimensions for the cross section, almost as if this beam were a strip of brass.

 

[Jonski]

Well, you provide some data, but not all which is necessary to analyze this problem.

How was the beam supported?
What were the dimensions of the beam (LxBxD)?
How was the cross section oriented with respect to the load?

Your inertia calculation suggests this beam was 40 cm wide and 3.18 mm thick. That's a very odd set of dimensions for the cross section, almost as if this beam were a strip of brass.

The cross section of the beam was 400mm long 3.18mm height and 19.02mm deep
The set up is shown below

 

[SteamKing]

The cross section of the beam was 400mm long 3.18mm height and 19.02mm deep
The set up is shown below

You used the wrong dimensions in the inertia calculation. The I is calculated for the cross section of the beam, which is normal to the length axis.

​

The moment of inertia for the beam in the figure above is I = ba³ / 12

 

[Jonski]

You used the wrong dimensions in the inertia calculation. The I is calculated for the cross section of the beam, which is normal to the length axis.

​

The moment of inertia for the beam in the figure above is I = ba³ / 12

Thanks, this really helped a lot

 

[PhanthomJay]

The problem I have is finding the correct moment of area as I think this is were I am getting it wrong. I have seen that for a rectangle it would be b*h^3/12
Then I = 0.4*0.00318^/12 = 1.07e-9 m^4

Isn't b equal to 19.02 mm??