A cantilever beam is subjected to a concentrated load of 2000N. The cross sectional dimensions of the double-tee beam are shown. Determine (a) the shear stress at point H, which is 17 mm below the centroid of the double-tee shape, (b) the shear stress at point K, which is 5 mm above the centroid of the double tee shape, and (c) the maximum horisontal shear stress in the double tee shape.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A cantilever beam is subjected to a concentrated load of 2000N. The cross sectional dimensions of the double-tee beam are shown. Determine (a) the shear stress at point H, which is 17 mm below the centroid of the double-tee shape, (b) the shear stress at point K, which is 5 mm above the centroid of the double tee shape, and (c) the maximum horisontal shear stress in the double tee shape.

### Diagram and Explanation:

The image consists of a 3D perspective and a schematic view of an I-beam, mounted horizontally and subjected to a vertical point load.

#### 3D Perspective:
- The I-beam is fixed at one end to a wall using four bolts and is subjected to a downward force of 2,000 N at its free end. 
- The axes are labeled with `y` pointing upwards, `z` pointing horizontally into the page, and `x` along the length of the beam.

#### Schematic Cross-section:
- The cross-section of the I-beam is T-shaped. The dimensions are given:
  - Total width of the top flange: 56 mm
  - Thickness of the top flange: 3 mm
  - Height of the web: 42 mm
  - Thickness of the web: 5 mm
  - Dimensions for the segments of the flange around the web are 20 mm each.
  
- Key points marked on the cross-section:
  - **Point K**: Located at the centroid of the beam section.
  - **Point H**: Positioned at 17 mm below the top flange, along the vertical web. 
  
### Calculation Fields:

- The shear stress at point **H**:
  
  |                                                 |                                                   |
  |-------------------------------------------------|---------------------------------------------------|
  | The shear stress at point **H**:                |                                                   |
  | The shear stress at point **K**:                |                                                   |
  | The maximum horizontal shear stress:            |                                                   |

These placeholders are meant for inputting calculated values of shear stress at specified points on the I-beam.
Transcribed Image Text:### Diagram and Explanation: The image consists of a 3D perspective and a schematic view of an I-beam, mounted horizontally and subjected to a vertical point load. #### 3D Perspective: - The I-beam is fixed at one end to a wall using four bolts and is subjected to a downward force of 2,000 N at its free end. - The axes are labeled with `y` pointing upwards, `z` pointing horizontally into the page, and `x` along the length of the beam. #### Schematic Cross-section: - The cross-section of the I-beam is T-shaped. The dimensions are given: - Total width of the top flange: 56 mm - Thickness of the top flange: 3 mm - Height of the web: 42 mm - Thickness of the web: 5 mm - Dimensions for the segments of the flange around the web are 20 mm each. - Key points marked on the cross-section: - **Point K**: Located at the centroid of the beam section. - **Point H**: Positioned at 17 mm below the top flange, along the vertical web. ### Calculation Fields: - The shear stress at point **H**: | | | |-------------------------------------------------|---------------------------------------------------| | The shear stress at point **H**: | | | The shear stress at point **K**: | | | The maximum horizontal shear stress: | | These placeholders are meant for inputting calculated values of shear stress at specified points on the I-beam.
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