Non-linear Temperature Gradient Part 3. Effects on Beams

February 8, 2024
BLOG BRIDGE INSIGHT

Nonlinear Temperature Effects on Beams

(1) Basic Concept

   Through Part 1 & 2, we looked at how the temperature gradient load of a bridge is calculated based on the design criteria. Now, let's examine how the calculated load affects the bridge deck.

   Temperature load will cause deformation in members, and in the case of members with free boundary conditions, no stress occurs due to temperature load.

   Based on the beam theory, when a cross-section is remain on a plane, temperature load deformation occurs in axial deformation and bending deformation.

 

Figure1. Deformation of a beam due to temperature load

Figure1. Deformation of a beam due to temperature load

 

   When both ends of a beam are restrained and subjected to temperature load, the following stresses are generated:

 

 

Figure2.

Figure2.

 

Figure3. Effects on constrained beams

Figure3. Effects on constrained beams

 

   Applying the above concept to non-linear temperature loads, even in a simply supported beam where all restraints are released, residual stress (self-equilibrating eigen stress) occurs in the beam. This can be seen as stress to maintain the equilibrium state of the member according to beam theory.

 

Figure4. Variation in stress for each stage

Figure4. Variation in stress for each stage

 

   Let's consider the below example to check how residual stress in a simply supported beam is calculated.

 

(2) Example

   Let's assume a beam with a length of L, a width of 1.2m, and a height of 1.5m is subjected to the following non-linear temperature load:

 

Figure5. Example Cross Section Details

Figure5. Example Cross Section Details

 

   When both ends are restrained, the stress produced in the cross-section is as follows:

 

Figure6. Restraint stress due to temperature loading

Figure6. Restraint stress due to temperature loading

 

   First, let's calculate the effect of axial restraint.

 

Figure7. Effect of axial restraint

Figure7. Effect of axial restraint

 

   

Secondly, when we calculate the effect of bending restraint, we can obtain the following results:

Figure7. Effect of axial restraint_preview2

 

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You can check more of these details in the download file.

 

(3) Validation of the example

(4) Conclusion

 

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About the Author
Jay.J | Structural Engineer | MIDAS IT HQ

I executed bridge (rail, road) projects over ten years as a structural engineer. I mainly did overseas projects in Kuwait, Indonesia, Malaysia, the Philippines, the U.K., etc. You know what? I've never been to the places on a business trip, even after completing construction. I have experienced national design-build projects twice and have done almost every shape of bridge project except wire bridges.

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