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Assessment 1 (Part B) (Online Submission) Student ID: 49325 CAMD: Computer-Aided Mechanical Design Student Name (First name Second name): Due 11:59PM, 28 March 2024 * THIS ASSIGNMENT SHOULD TAKE AN AVERAGE STUDENT 4 HOURS TO COMPLETE. Question 1: For a two-dimensional plane truss structure, all the truss members have a uniform cross- sectional area of $A = 100 \text{ mm}^2$ and are made of material with Young's Modulus $E = 100 \text{ GPa}$. The truss consists of three plane elements, with space orientations $\theta$ and lengths $L$, as indicated in Figure 1. Two roller supports are applied at node No. 1 and node No. 2, respectively. Using the finite element method and hand calculations, determine: 1. Displacements at the global nodal positions No. 1 and No. 2. 2. Reaction forces at the node No. 3. Formulas: if we define $l = \cos\theta$ and $m = \sin\theta$, the general formulation of the stiffness matrix for any of the truss element can be given as follows: $\begin{bmatrix} l^2 & lm & -l^2 & -lm\\ lm & m^2 & -lm & -m^2\\ -l^2 & -lm & l^2 & lm\\ -lm & -m^2 & lm & m^2 \end{bmatrix} = \frac{AE}{L}$

          Assessment 1 (Part B)
(Online Submission)
Student ID:
49325 CAMD: Computer-Aided Mechanical Design
Student Name (First name Second name):
Due 11:59PM, 28 March 2024
* THIS ASSIGNMENT SHOULD TAKE AN AVERAGE STUDENT 4 HOURS TO COMPLETE.
Question 1: For a two-dimensional plane truss structure, all the truss members have a uniform cross-
sectional area of $A = 100 \text{ mm}^2$ and are made of material with Young's Modulus $E = 100 \text{ GPa}$. The
truss consists of three plane elements, with space orientations $\theta$ and lengths $L$, as indicated in Figure
1. Two roller supports are applied at node No. 1 and node No. 2, respectively.
Using the finite element method and hand calculations, determine:
1. Displacements at the global nodal positions No. 1 and No. 2.
2. Reaction forces at the node No. 3.
Formulas: if we define $l = \cos\theta$ and $m = \sin\theta$, the general formulation of the stiffness matrix for any of
the truss element can be given as follows:
$\begin{bmatrix} l^2 & lm & -l^2 & -lm\\ lm & m^2 & -lm & -m^2\\ -l^2 & -lm & l^2 & lm\\ -lm & -m^2 & lm & m^2 \end{bmatrix} = \frac{AE}{L}$

Assessment 1 (Part B)
(Online Submission)
Student ID:
49325 CAMD: Computer-Aided Mechanical Design
Student Name (First name Second name):
Due 11:59PM, 28 March 2024
* THIS ASSIGNMENT SHOULD TAKE AN AVERAGE STUDENT 4 HOURS TO COMPLETE.
Question 1: For a two-dimensional plane truss structure, all the truss members have a uniform cross-
sectional area of A = 100 mm^2 and are made of material with Young's Modulus E = 100 GPa. The
truss consists of three plane elements, with space orientations θ and lengths L, as indicated in Figure
1. Two roller supports are applied at node No. 1 and node No. 2, respectively.
Using the finite element method and hand calculations, determine:
1. Displacements at the global nodal positions No. 1 and No. 2.
2. Reaction forces at the node No. 3.
Formulas: if we define l = cosθ and m = sinθ, the general formulation of the stiffness matrix for any of
the truss element can be given as follows:
< b m a t r i x >
= (AE)/(L)

Added by Alec F.

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