Problem 2: Fixed-guided-in-Y beam
The equations for all 3 thermal load cases are shown below, the colors represent temperature field (white is high and black is low). The equations give the axial deformation u of the beam, the deflection w of the beam, and the axial stresses in the beam.
 | Boundary Conditions: u (x=0) = 0 w (x=0) = 0 β (x=0) = 0 u (x=L) = 0 β (x=L) = 0 D (x=L) = 0 |
The figure of the deformed beam illustrates the deflection resulting from load case C. Colors represent the axial stress field (green is zero, red is positive and blue is negative). Note that the boundary effects as shown in the figure is not included in the equations!
| Name | Symbol | Units | Description |
| Shear force | D | N | Internal shear force as function of the longitudinal direction (x) |
| Young’s modulus | E | N/m2 | Young’s modulus of the material |
| Axial force | F | N | Internal axial force as function of the longitudinal direction (x) |
| Height | H | m | The total length of the beam |
| Length | L | m | The total length of the beam in longitudinal direction |
| Moment | M | N/m | Internal moment as function of the longitudinal direction (x) |
| Temperature | ΔT | K | The biggest temperature difference in the beam |
| Axial deformation | u | m | Axial deformation of the beam as function of the longitudinal direction (x) |
| Deflection | w | m | Deflection of the beam as function of the longitudinal direction (x) |
| CTE | α | K-1 | Coefficient of thermal expansion (CTE) of the material |
| Rotation | β | rad | Rotation of the beam as function of the longitudinal direction (x) |
| Axial stress | σx | m | Axial stress of the beam, i.e. combined thermal and mechanical stress, as function of the longitudinal direction and the direction perpendicular (x and y) |
References
February 9 at Mikrocentrum. This event is organized in Dutch
Read more
The organizing committee invites you to submit a short abstract for a 20 minutes presentation and publication in the conference proceedings. Note that due to the limited number of presentations, it may be necessary to change the status from paper…
Read more
This symposium is intended for engineers and architects participating in or interested in the design and building of optical hardware. It is a great moment to network, to meet technical peers, and to visit the expo.
Read more