Deflection of Fixed Rotated Beam

• roldy
In summary, the beam is rotated 90 degrees so that the flanges are vertical and it has a loading of a 40' long 18" diameter pipe filled with water. The beam has a moment of inertia of 7.1099*10-5 m4 and a deflection of 0.149 m.
roldy
Homework Statement
What is the deflection of a fixed 40' beam that is rotated 90 degrees so that the flanges are vertical with a loading of a 40' long 18" diameter pipe filled with water? The beam is W14 x 30
Relevant Equations
V=A*L
A=pi*D^2/4
m=rho*V
W=m*g
I=1/12 * b*h^3
deflection = wL^3/(24EI)
W14 x 30:
d = 13.84" = 0.352 m
w = 6.730" = 0.171 m
tw = 0.270 = 0.00686 m
tf = 0.385 = 0.00978 m

40' = 12.192 m
18" = 0.4572 m
ρ = 997 kg/m3
E = 1.4*109

Calculate Weight of water:
V = A*L = π*(0.4572)2/4 *12.192 = 2.0016m3
W = m*g = ρ*V*g = 997*2.0016*9.81 = 19.576kN uniformally distributed load

Calculate moment of inertia of beam:
I = 1/12*b*h3 = Iflanges + Iinside = 2*[1/12*0.00978*0.3523] + [1/12*(0.352-0.00978)*0.006863] = 7.1099*10-5 m4

Calculate deflection of beam:
δ = wL3/(24EI) = 19.576*12.1923/(24*1.4*109*7.1099*10-5) = 0.149 m

Is my process correct? I've never done a rotated I-beam before.

roldy said:
Problem Statement: What is the deflection of a fixed 40' beam that is rotated 90 degrees so that the flanges are vertical with a loading of a 40' long 18" diameter pipe filled with water? The beam is W14 x 30
Relevant Equations: V=A*L
A=pi*D^2/4
m=rho*V
W=m*g
I=1/12 * b*h^3
deflection = wL^3/(24EI)

W14 x 30:
d = 13.84" = 0.352 m
w = 6.730" = 0.171 m
tw = 0.270 = 0.00686 m
tf = 0.385 = 0.00978 m

40' = 12.192 m
18" = 0.4572 m
ρ = 997 kg/m3
E = 1.4*109

Calculate Weight of water:
V = A*L = π*(0.4572)2/4 *12.192 = 2.0016m3
W = m*g = ρ*V*g = 997*2.0016*9.81 = 19.576kN uniformally distributed load

Calculate moment of inertia of beam:
I = 1/12*b*h3 = Iflanges + Iinside = 2*[1/12*0.00978*0.3523] + [1/12*(0.352-0.00978)*0.006863] = 7.1099*10-5 m4

Calculate deflection of beam:
δ = wL3/(24EI) = 19.576*12.1923/(24*1.4*109*7.1099*10-5) = 0.149 m

Is my process correct? I've never done a rotated I-beam before.
I am not going to check all the numbers, but the method looks ok except for one thing I do not understand. What is the Iinside term? If I understand the set-up, it is an H cross-section, with the uprights covered by the Iflanges term. If the Iinside is for the horizontal part then where does (0.352-0.00978) come from?

That value is the "length" of the horizontal part. Depth of the beam subtract the flange widths. I made a mistake, the value should actually be 0.352 - 2×0.00978.

roldy said:
That value is the "length" of the horizontal part. Depth of the beam subtract the flange widths. I made a mistake, the value should actually be 0.352 - 2×0.00978.
Ok. I think I would just have assumed the contribution from that was negligible (which it is).
The given data are to only two significant figures, so I would give the answer to the same precision.

I have no idea why you changed to SI units. No need to when you are dealing with the USA standard beams. Otherwise, the depth of a beam is measured between the far edges of each flange. Your beam is rotated along the weak axis, so check your values for appropriate dimensions when calculating the moment of inertia.

1. What is deflection of a fixed rotated beam?

Deflection of a fixed rotated beam is a measure of the amount of bending or deformation that occurs in a beam when a load is applied to it. It is an important concept in structural engineering and is used to ensure the safety and stability of structures.

2. How is deflection of a fixed rotated beam calculated?

The deflection of a fixed rotated beam can be calculated using the Euler-Bernoulli beam theory, which takes into account the dimensions of the beam, the material properties, and the magnitude and location of the applied load. There are also various computer programs and software that can be used to calculate the deflection of a beam.

3. What factors affect the deflection of a fixed rotated beam?

The deflection of a fixed rotated beam is affected by several factors, including the material properties of the beam (such as the modulus of elasticity and moment of inertia), the length and cross-sectional area of the beam, the type and location of the applied load, and any supports or restraints present.

4. Can the deflection of a fixed rotated beam be controlled?

Yes, the deflection of a fixed rotated beam can be controlled by adjusting the design and dimensions of the beam, as well as the location and magnitude of the applied load. Additional supports and restraints can also be added to limit the amount of deflection in a beam.

5. Why is it important to consider deflection in the design of structures?

It is important to consider deflection in the design of structures because excessive deflection can lead to structural failure and compromise the safety and stability of the structure. By calculating and controlling the deflection, engineers can ensure that a structure can withstand the expected loads and maintain its integrity over time.