## Question

**What are the differences between Temperature Gradient and Beam Section Temperature?**

## Answer

**There are differences between Temperature Gradient and Beam Section Temperature.**

First, let's explain Beam Section Temperature

Beam Section Temperature is used to input temperature differences within the cross-section of a beam element. It is employed in structures like arches, beams, slabs, or decks where variations in temperature across the cross-section need to be considered. This is especially useful when dealing with situations like sunlight exposure on reinforced concrete arches, beams, or floor decks.

midas Civil에서 Beam section temperature 입력을 하는 기준은 다음 그림과 같이 표현 됩니다.

The values for H1, H2, T1, and T2 are input from the reference position, allowing you to represent temperature differences within the section.

Now, let's discuss Temperature Gradient

Temperature gradient loading can be performed on beam and plate elements where bending stiffness can be considered. For beam elements, you enter the temperature difference and distance between the outermost angles of the y and z axes based on the element coordinate system, and for plate elements, you enter the temperature difference between the top and bottom surfaces of the plate and the plate thickness.

The temperature difference between the top and bottom surfaces gives rise to the following equivalent moments

where α is the linear expansion coefficient, E is the elastic modulus, I is the section secondary moment about the corresponding axis of the element, ΔT is the temperature difference at the outermost edge, h is the distance between the outermost edges of the element cross-section, t is the thickness of the plate element, and ν is Poisson's Ratio. For example, in the Section Property shown in the figure below, Czp and Czm are the stress range of Sbz (y value of Bending Stress in the figure above), Cyp and Cym are the stress range of Sby, and Qyb and Qzb correspond to Q/b values in the y and z axes in the figure above. Please see the imge below.

As you can see, you can enter the temperature difference between the top and bottom, so the difference with the beam section temperature is that the temperature is always zero at the center axis. So you're only going to have a moment due to the temperature difference, not an axial force.

To show a simple example, we have created a beam element with fixed ends as follows.

First, we used the Temperature gradient load to input a temperature difference of 50 degrees between the top and bottom in the z-axis direction. If we were to represent this part pictorially, it would look like this.

Then, we used another temperature load, Beam section temperature, to apply a temperature of 50 degrees at the top and 0 degrees at the bottom where the sunlight does not reach.

Even though there is a 50 degree temperature difference between the top and bottom, there is a difference in the member forces caused by the different temperature distribution shape. In both cases, the moment generated is the same because the temperature difference between the upper and lower parts is the same at 50 degrees, but in the case of a temperature gradient, no axial force is generated. You should consider this difference when using the function.

Temperature gradient and moment from beam section temperature (same) (unit: kN)

Shear force diagram of Temperature gradient (No shear force is generated) (Unit: kN)

Shear force diagram of Beam section temperature (shear force generated) (Unit: kN x m)

Compare the results of Temperature gradient and Beam section temperature functions

기능 | Temperature gradient | Beam section temperature |

Shear Force(kN) | 9.6 | 9.6 |

Moment (kNxm) |
- | -288 |