The beam shown has an overall length of L = 5 m and is subjected to the load shown where w = 9 kN/m. Determine the smallest web thickness, t, for the beam if the maximum shear stress cannot exceed 14 MPa. Express your answer in mm to the nearest 0.1 mm.
The beam shown has an overall length of L = 5 m and is subjected to the load shown where w = 9 kN/m. Determine the smallest web thickness, t, for the beam if the maximum shear stress cannot exceed 14 MPa. Express your answer in mm to the nearest 0.1 mm.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The beam shown has an overall length of L = 5 m and is subjected to the load shown where w = 9 kN/m. Determine the smallest web thickness, t, for the beam if the maximum shear stress cannot exceed 14 MPa. Express your answer in mm to the nearest 0.1 mm.
Transcribed Image Text:The image depicts a structural beam diagram and its cross-sectional shape. Here is a detailed description for educational purposes:
### Beam Diagram
- The beam is supported at two points: a pin support at point \( A \) and a roller support at point \( B \).
- The beam is subjected to a varying distributed load, denoted by arrows, increasing from left to right across the beam.
- The load density is represented by the symbol \( w \) and is triangularly distributed, with the maximum load at point \( B \).
- The length of the beam from \( A \) to \( B \) is divided into segments: \( L/2 \) from \( A \) to the midpoint, and \( L/4 \) from the midpoint to point \( C \) and from \( C \) to \( B \).
### Cross-Section Diagram
- The beam's cross-section is a T-shape.
- The total height of the cross-section is 150 mm.
- The width of the flange (top horizontal part of the T) is \( 5t \).
- The height of the web (vertical part of the T) is shown as 30 mm.
- The thickness of both the flange and the web is denoted as \( t \).
This illustration helps in analyzing the structural behavior of the beam under a non-uniform load, vital for understanding concepts in statics and structural engineering.
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