Application of Temperature effects

[nicoCTQNU]

Hi Everyone.

I have a simple post tensioned beam design with loads that I extracted from a grillage model

I would just like to know if I am applying the loads correctly to the beam.

Below are the loads as received from ASBD:

The loads are then added to the beam loads as two seperated cases, one for positive and one for negative.  The loads are then manually inserted under SLS for both axial and Moment since this check only applies to SLS.  

Since the temperature effect is for the entire cross section, it surely means that it is true for the entire length of beam.

I also ignored reinforcement during for the loads.

Is this correct so far?

[dave_geeves]

Hi Nico,

I don't believe you have quite got it right in the application of differential temperature  loads to your beams.

Differential temperature effects are split into two components

1. Primary effect - which are the self equilibrating stresses in the beam due to a given temperature profile where there will be no moments and forces in the beam so the secondary effects (the values in the diff temp loading table in the design beam) will be zero.
2. If the girder has redundancy (eg is two span continuous), which I believe is what you have, then there will be secondary effects as the central support is restraining the deflection at this point.  The secondary moment (the values in the diff temp loading table of the design beam) will be zero at the free ends and will rise linearly to a value over the continuous pier.

When the beam is designed for serviceability then the stress summary table should show two values of diff temp effects, one the primary (self equilibrating) effect and the other the secondary effect due to redundancy.

To obtain the secondary effect from your grillage you will need to run an additional load case (in fact two, one for heating one for cooling) where you have applied beam element  temperature loads to the main girders (membrane and gradient) that will be equivalent to the negative of the  relaxing moments and forces given in the  tables you show in your post.  These will be the same all along the beam if the section is the same.

The equivalent membrane and gradient temperature can easily be obtained by a simple calculation where you need to know the cross section area and the moment of inertia of the section.  You can find these calculations in the "Technical Advices Notes" on my website.

I hope this has answered your query so please mark my reply as a solution if it has done so. Thanks.

Kind regards

Dave Geeves

[nicoCTQNU]

HI Dave,

Thanks for the reply, I just want to make 100% sure I understand:

When I analyse the beam for differential  temperature for my specific beam profile (M5beam with precast slab section on top), I'm presented with the windows below.  So regarding the stresses:

Primary stresses:  Stresses within the cross section that are generated from a specific temperature profile which keeps the section in check and is presented below.

Secondary Stresses:  

The figure below then displays the following forces if the beam is restrained for its entire length:

Heating: 

• Axial = 627kN (Compression)
• Moment = 218kNm (sagging)

Cooling:

• Axial = 744kN (Tension)
• Moment = 29.9kNm (Hogging)

Is the above correct so far?

Second clarification:  When you say "....that will be equivalent to the negative of the  relaxing moments and forces given in the  tables you show in your post." - Is that because the sign convention is reversed between the results and load application?

I'm assuming the the additional load cases you are referring to below is applying loads to the actual grillage (not as I have done it above), whereby I can export those loads and transfer it to my beam file(remember I have a separate file with my loads)? (I have added my grillage model)

Im also not sure what to add them then as.  There are 3 temperature loads that I can add under beam load.  Top on is

• Temperature Primary Moment

For the Heating moment, I would do it as below and apply it to all the longitudinal beams.  Basically applying a sagging moment in the centre of the beam.

I'm not sure where to apply the axial load.

[dave_geeves · Accepted solution]

Hi Nico,

You are right in most of what you say.

In my technical advice note I say that there are a number of different ways of applying the diff temp loading to a grillage.  You have chosen the first method using "Primary thermal moments", which does not allow the application of thermal primary axial forces.  However this is ok for your structure as it has no redundancies and therefore the primary axial force will have no effect as it will just expand (or contract) the deck in a longitudinal direction without generating any effects.  Also with this method, you should apply the relaxing moments (as shown in your output) so you will not reverse the sign.  these should be applied as uniform moments along the whole beam length.  You will need two rows in this table, one for the edge beams and the other for the internal beams

You will need to create two separate load cases, one for heating the other for cooling.

For grillages that do have redundancies, then the third method should be used where the primary "relaxing" moments and forces are changed to "Restraining" moments and forces, by changing the sign, and  are converted to equivalent membrane and gradient temperatures (as detailed in my technical advice note).  These can then be applied as "Beam element temperature loads" where the axial and gradient affects can be added as temperatures in the same load case.  You will still need two load cases, one for heating the other for cooling.

I hope this has helped.

Kind regards

Dave Geeves