# Straight beam

## 1 Model

For this test, a cantilever beam with a solid rectangular cross section is foxed on one end and a force is applied onto the other end. The beam is shown in the figure below:

The length of the beam is
$$L = 6\text{ m}$$
, the height and the width of the cross section are
$$h=0.2\text{ m}$$
and
$$w=0.1\text{ m}$$
, respectively. The Elastic modulus is
$$E=10\cdot10^6\text{ Pa}$$
and the Poisson ratio is
$$\nu = 0.3$$

## 2 Benchmark

### 2.1 Extension

For this benchmark, a force
$$F = 1\text{ N}$$
is applied in the x-direction at the tip of the beam, as shown in the figure below:

According to Macneal et al. (1985), the expected displacement of the tip in the x-direction is
$$d_x = 3.0\cdot10^{-5}\text{ m}$$
.

### 2.2 In-plane shear

For this benchmark, a force
$$F_z = -1\text{ N}$$
is applied in the z-direction, as shown in the figure below:

According to Macneal et al. (1985), the expected displacement of the tip in the z-direction is
$$d_z = -0.1081\text{ m}$$
.

### 2.3 Out-of-plane shear

For this benchmark, a force
$$F_y = 1\text{ N}$$
is applied in the y-direction, as shown in the figure below:

According to Macneal et al. (1985), the expected displacement of the tip in the y-direction is
$$0.4321\text{ m}$$
.

### 2.4 Twist

For this benchmark, a moment
$$M_x = 1\text{ Nm}$$
is applied around the x-axis, as shown in the figure below:

According to Macneal et al. (1985), the expected rotation of the tip around the x-axis is
$$r_u = 1.878\text{ deg}$$
.

## 3 Results

The tests are considered passed when the last 20% of the time series from Ashes is within 1% of the results from Macneal et al. (1985)

The report for this test can be found on the following link:

Note: for the Twist load case, a larger difference is expected since Ashes does not include warping. For this load case, a 7% difference is considered passed.