Determine a suitable size beam (gantry girder)

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Discussion Overview

The discussion revolves around determining a suitable size for a gantry girder beam based on specified maximum bending stress and modulus of elasticity. Participants explore methods for calculating the required beam size, referencing standard sections tables and discussing the implications of beam geometry on stress calculations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant outlines the problem, specifying maximum bending stress and modulus of elasticity, and expresses uncertainty in applying the formulas due to a lack of specific cross-section information for the gantry girder.
  • Another participant requests the cross-section details, noting that 'gantry girder' is a vague term that complicates the analysis.
  • A participant mentions the use of a British standards table that includes various beam types, indicating that the absence of a specified cross-section is a source of confusion.
  • One suggestion is to calculate the section modulus required to meet the maximum allowable bending stress and then reference the tables for a suitable beam.
  • A question is raised about whether the calculation method for section modulus is the same as that for universal beams, indicating a need for clarification on the differences in beam types.
  • Another participant clarifies that gantry beam sections are not symmetric with respect to the neutral axis, emphasizing the importance of using the correct section modulus value from the tables and the relationship between bending stress and section modulus.

Areas of Agreement / Disagreement

Participants generally agree on the need to calculate the section modulus and reference standard tables, but there is disagreement regarding the specifics of the calculations and the implications of the beam's geometry. The discussion remains unresolved as participants seek further clarification and information.

Contextual Notes

The discussion highlights limitations related to the lack of specific cross-section information and the potential differences in calculation methods for various beam types. Participants express uncertainty about applying standard formulas to gantry girders compared to universal beams.

hershl
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Homework Statement


In cross-section, the beam you are working on is a gantry girder.The maximum bending stress in the girder must not exceed 25MN/m2 and the modulus of elasticity can be assumed to be 210GN/m2.
Determine a suitable size for the beam, selected from the standard sections tables.
Also determine the maximum stress of the chosen beam and its radius of curvature.


Homework Equations



E=σ=M
R y I

The Attempt at a Solution


I have worked out the max bending moment as 36KN and drawn the SFD and BMD

Using the formula
σmax=M*ymax
I
This is where i get stuck as the notes i have are for universal beams and not gantry girders

I'm not after the answer but if anyone can shine some light on how to go about solving this i'd be much appreciative.

The course is HNC electronic and electrical eng. With a mechanical principles module
 
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Can you post the cross-section? I'm afraid 'gantry girder' is a rather vague description.
 
Sorry
The table comes from a British standards book. showing universal, structural tees and gantry girders.
There is no cross section stated in the question(i think this is where I'm getting stuck as i have examples using the cross section).

Here is that table as well as my working of the SFD and BMD.

Thanks
 

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I would work out the section modulus of the girder required to meet the max. allowable bending stress and then use the tables labeled 'gantry girder' to find a candidate beam.
 
Is that worked out using the same "max bending moment times 1/2 of depth of beam over 2nd moment of area"
As you would with the universal beam?
 
The gantry beam sections are not symmetric w.r.t. the neutral axis of the beam. This is clearly shown in the cross section sketches of the attached tables. The section modulus value Z from the beam tables should be the minimum value for a given beam size, and they can be checked by using the appropriate I and y values (Z = I / y). The bending stress is calculated as σ = M / Z, using appropriate units of course.
 
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