Solving Beam Bending Qs: Find Beam Dimensions with 25 MNm^2 Stiffness

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SUMMARY

The discussion focuses on calculating the dimensions of a steel beam with a flexural stiffness of 25 MNm². The user initially calculated the moment of inertia (I) using the formula I = bd³/12, assuming a breadth (b) of 50mm, which led to an incorrect depth (d) of 31.072mm. The correct approach involves converting units properly, resulting in a recalculated depth of approximately 310.7mm. This highlights the importance of accurate unit handling in structural calculations.

PREREQUISITES
  • Understanding of flexural stiffness and its significance in beam design.
  • Familiarity with the moment of inertia formula I = bd³/12 for rectangular cross-sections.
  • Knowledge of unit conversions, particularly between metric units (N, m, mm).
  • Basic principles of material properties, specifically Young's modulus for steel (200 GPa).
NEXT STEPS
  • Study the implications of flexural stiffness in beam design and its applications in engineering.
  • Learn advanced unit conversion techniques relevant to structural engineering calculations.
  • Explore finite element analysis (FEA) tools for validating beam design results.
  • Investigate the effects of varying beam cross-sections on moment of inertia and stiffness.
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in beam design and analysis will benefit from this discussion, particularly those focusing on accurate calculations and unit conversions in structural mechanics.

HorseRidingTic
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Bonjouro!
Firstly, as this is my first post here, I would like to say thank you to everyone who is a part of the site and Hello!
I've used this forum a number of times, but this is the first time I've posted here as this user!

If the flexural stiffness of a beam is 25 MNm^2, and the beam is made of steel, what is the breadth and depth of the beam (or at least beam dimensions that would work)

I did this by saying
I = bd^3/12

EI = 25,000,000,000 Nmm^2
E = 200,000 MPa
I = 1,500,000mm^4
Using I = b*d^3 / 12
Assuming breadth (b) is 50mm, I get depth (d) as 31.072mm, but apparently this is wrong and I cannot figure out why :'(

My question comes from this thing I found on the internet, which gives me these FEA results, but they don't match up!
View post on imgur.com

Please help PhysicsForum guys! You're my only hope!
 
Last edited:
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HorseRidingTic said:
Bonjouro!
Firstly, as this is my first post here, I would like to say thank you to everyone who is a part of the site and Hello!
I've used this forum a number of times, but this is the first time I've posted here as this user!

If the flexural stiffness of a beam is 25 MNm^2, and the beam is made of steel, what is the breadth and depth of the beam (or at least beam dimensions that would work)

I did this by saying
I = bd^3/12

EI = 25,000,000,000 Nmm^2
E = 200,000 MPa
I = 1,500,000mm^4
Using I = b*d^3 / 12
Assuming breadth (b) is 50mm, I get depth (d) as 31.072mm, but apparently this is wrong and I cannot figure out why :'(

My question comes from this thing I found on the internet, which gives me these FEA results, but they don't match up!
View post on imgur.com

Please help PhysicsForum guys! You're my only hope!
I think your problem comes down to a mistake in handling the units of EI and E somewhere.

Let's take the original data:

EI = 25 MN-m2, where E = 200 GPa = 200 × 109 N/m2

By dividing EI by E, we get:

I = EI / E = 25 × 106 N-m2 / (200 × 109 N/m2) = 1.25 × 10-4 m4

Since there are 103 mm / m, there are 1012 mm4/m4

So I = 1.25 × 10-4 m4 = 1.25 × 10-4 m4 ⋅ 1012 mm4/m4 = 1.25 × 108 mm4

taking b = 50 mm and assuming a rectangular cross-section for I:

I = bh3 / 12 = 50h3 / 12 = 1.25 × 108 mm4

h3 = 3 × 107 mm3

h ≈ 310.7 mm
 
Brother! You have saved me. iT was the units, that were the issue. Now I know better. Thank you!
 

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