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**Task:**

The task is to check the following construction using two basic design methodologies:

- Deflection should not exceed 15mm over the length of the model.
- Maximum stress should not exceed 50% of ultimate tensile stress.

*Figure 1 – Initial model*

The initial design model consists of 5 box sections at 280x280x10 mm and channels with l=10000 mm and h=380 mm. The material for all of our elements is considered to be carbon steel. Our main goal is to check whether the initial design satisfies all of our conditions and provide some improvements if not.

The initial design model consists of 5 box sections at 280x280x10 mm and channels with l=10000 mm and h=380 mm. The material for all of our elements is considered to be carbon steel. Our main goal is to check whether the initial design satisfies all of our conditions and provide some improvements if not.

**Solution:**

We consider several basic assumptions for this analysis.

- The body is homogeneous: it is made of the same material in all its parts.
- The body is isotropic: the properties of the material do not depend on direction.
- The cross section is constant.
- We consider only elastic behavior of the material without plastic deformations.

**Analysis plan****:**

The material is assumed to be carbon steel with the following properties:

*Figure 2 – Material properties*

We considered standard triangle node elements for our mesh. Size parameters and the esh are shown below:

*Figure 4 – Generated mesh*

Boundary conditions:

We have fixed support boundary conditions on all 4 edges of the channels:

*Figure 5 – Boundary conditions*

Load conditions:

Case 1: All of the weight is hogging on the middle axle.

*Figure 6 – Loads*

Case 2: Front and back axles are taking all of the weight.

*Figure 7 – Loads*

Possible errors could occur because of improperly generated mesh and inaccuracy between assumed and real boundary/load conditions and our model.

**Results:**

Case 1, Von-Mises Stress, MPa:

*Figure 8 – Case 1, Von-Mises Stress, MPa*

*Figure 9– Case 1, Maximal Von-Mises Stress zone*

Case 1, Von-Mises Deformations, mm:

*Figure 10 – Case 1, Von-Mises Deformations, mm*

Case 2, Von-Mises Stress, MPa:

*Figure 11 – Case 2, Von-Mises Stress, MPa*

Case 2, Von-Mises Deformations, mm:

*Figure 12 – Case 2, Von-Mises Deformations, mm*

**CONCLUSIONS**

For Case 1, if we neglect the boundary zone and check other maximal values from different locations, we will see that the maximal value of stress is about 26-32 MPa. Therefore we will use the average of these values for the comparison table. It doesn’t influence the allowable value, because maximal stress doesn’t exceed the allowable 50% of ultimate stress. Also, maximal deformations don’t exceed the allowable 15 mm.

*Table 1*

Parameter | Value |

Von-Mises stress,MPa (Case 1) | 28 |

Von-Mises stress, MPa (Case 2) | 20 |

Von-Mises deformations, mm (Case 1) | 2.08 |

Von-Mises deformations, mm (Case 2) | 0.69 |

For Case 2, we see that our stress values decreased. This happened because we had distributed our load near the boundary zone, which caused decreasing distances between acting forces and the fixed zone, i.e. decreasing of moments. Deformations have also become three times smaller.

Both of our cases satisfy design conditions that were mentioned in the task objectives section, therefore no improvements are necessary and we can accept our initial design.