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The double T-beam is fabricated from Aluminum that has allowable stresses of allow = 162 MPa and Tallow = 105 MPa. Determine: a) The maximum allowable bending moment that can be applied to the section. b) The maximum allowable shear force that can be applied to the section. 25 mm 175 mm 75 mm 75 mm 75 mm 25 mm 25 mm

The double T-beam is fabricated from Aluminum that has allowable stresses of allow = 162 MPa and Tallow = 105 MPa. Determine: a) The maximum allowable bending moment that can be applied to the section. b) The maximum allowable shear force that can be applied to the section. 25 mm 175 mm 75 mm 75 mm 75 mm 25 mm 25 mm

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**T-Beam Design Analysis** The double T-beam illustrated is fabricated from aluminum. For this beam, the material has allowable stresses where the allowable normal stress (\( \sigma_{\text{allow}} \)) is 162 MPa, and the allowable shear stress (\( \tau_{\text{allow}} \)) is 105 MPa. This analysis aims to determine: a) The maximum allowable bending moment that can be applied to the section. b) The maximum allowable shear force that can be applied to the section. **Beam Dimensions and Structure:** The diagram presents a cross-section of the T-beam with the following dimensions: - The total height of the beam is 175 mm. - The flange (top horizontal part) of the beam has a thickness of 25 mm. - The overall width of the entire beam is composed of two segments each 75 mm wide, separated by 75 mm, making the total width of the top flange 225 mm. - The web (vertical part) of each T-segment is 25 mm thick. **Structural Analysis:** 1. **Flange Dimensions:** - Width: 75 mm per segment - Thickness: 25 mm 2. **Web Dimensions:** - Height: 175 mm - Thickness: 25 mm These dimensions are critical for calculating the moment of inertia and section modulus, which will be used in determining the maximum bending moment and shear force. The symmetry and uniformity of the T-beam suggest that calculations will consider contributions from both the flange and web sections to find these limits efficiently. To provide practical guidance for further calculations, engineers should consider these structural characteristics and constraints while analyzing the beam's performance under load.
Transcribed Image Text:**T-Beam Design Analysis** The double T-beam illustrated is fabricated from aluminum. For this beam, the material has allowable stresses where the allowable normal stress (\( \sigma_{\text{allow}} \)) is 162 MPa, and the allowable shear stress (\( \tau_{\text{allow}} \)) is 105 MPa. This analysis aims to determine: a) The maximum allowable bending moment that can be applied to the section. b) The maximum allowable shear force that can be applied to the section. **Beam Dimensions and Structure:** The diagram presents a cross-section of the T-beam with the following dimensions: - The total height of the beam is 175 mm. - The flange (top horizontal part) of the beam has a thickness of 25 mm. - The overall width of the entire beam is composed of two segments each 75 mm wide, separated by 75 mm, making the total width of the top flange 225 mm. - The web (vertical part) of each T-segment is 25 mm thick. **Structural Analysis:** 1. **Flange Dimensions:** - Width: 75 mm per segment - Thickness: 25 mm 2. **Web Dimensions:** - Height: 175 mm - Thickness: 25 mm These dimensions are critical for calculating the moment of inertia and section modulus, which will be used in determining the maximum bending moment and shear force. The symmetry and uniformity of the T-beam suggest that calculations will consider contributions from both the flange and web sections to find these limits efficiently. To provide practical guidance for further calculations, engineers should consider these structural characteristics and constraints while analyzing the beam's performance under load.
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