Breslau's principle. $$ A B=3 \mathrm{~m}, B C=4 \mathrm{~m} $$. El is constant. Draw the influence line diagram for the propped reaction of a propped cantilever beam having span 6 m . Take $$ E I= $$ constant.

Question

UpStudy AI · Accepted Answer

To draw the influence line diagram for the propped reaction of a propped cantilever beam with a span of 6 m, we will follow these steps:

1. **Identify the Beam Configuration**: 
   - The beam is a propped cantilever, which means it is fixed at one end (let's call it point A) and simply supported at the other end (point B).
   - The span $$ AB = 6 \, \text{m} $$.

2. **Determine the Reaction Forces**:
   - The propped reaction at point B will be denoted as $$ R_B $$.
   - The fixed end at point A will have a vertical reaction $$ R_A $$ and a moment $$ M_A $$.

3. **Influence Line for Reaction at B**:
   - The influence line for the reaction at B is determined by moving a unit load across the length of the beam and observing the effect on the reaction at B.

4. **Calculate the Influence Line**:
   - When the unit load is placed at a distance $$ x $$ from A (where $$ 0 \leq x \leq 6 $$), the influence line for the reaction at B can be calculated using the principles of static equilibrium.

5. **Influence Line Equation**:
   - The influence line for the reaction at B can be derived as follows:
     - For a unit load at a distance $$ x $$ from A, the reaction at B can be expressed as:
     $$
     R_B = \frac{L - x}{L}
     $$
     where $$ L $$ is the total length of the beam (6 m in this case).

6. **Plotting the Influence Line**:
   - The influence line will be a straight line starting from $$ R_B = 1 $$ when the load is at point A (0 m) and decreasing linearly to $$ R_B = 0 $$ when the load is at point B (6 m).

Now, let's summarize the influence line for the reaction at B:

- At $$ x = 0 \, \text{m} $$: $$ R_B = 1 $$
- At $$ x = 6 \, \text{m} $$: $$ R_B = 0 $$

The influence line diagram will be a straight line from (0, 1) to (6, 0).

### Influence Line Diagram
- The x-axis represents the position along the beam (from A to B).
- The y-axis represents the reaction at B due to a unit load.

This influence line can be drawn on a graph with the specified coordinates. If you need a visual representation, please let me know!
To draw the influence line for the reaction at point B of a propped cantilever beam with a 6-meter span: 1. **Beam Configuration**: Fixed at point A and simply supported at point B. 2. **Influence Line**: A straight line from (0, 1) to (6, 0), where: - At 0 meters (point A), the reaction at B is 1. - At 6 meters (point B), the reaction at B is 0. 3. **Graph**: Plot this line on a graph with the x-axis representing the beam length and the y-axis representing the reaction at B. This line shows how the reaction at B changes as a unit load moves along the beam.

Breslau’s principle. . El is constant.
Draw the influence line diagram for the propped reaction of a propped cantilever beam having span 6 m .
Take constant.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Engineering Questions

Breslau’s principle. . El is constant. Draw the influence line diagram for the propped reaction of a propped cantilever beam having span 6 m . Take constant.