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Two steel plates (A572, Fy = 50 ksi) are welded together to form an inverted T-beam. Determine the maximum bending stress developed. Also determine the maximum shear stress at the neutral axis of the cross-section and at the intersection

Two steel plates (A572, Fy = 50 ksi) are welded together to form an inverted T-beam. Determine the maximum bending stress developed. Also determine the maximum shear stress at the neutral axis of the cross-section and at the intersection

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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Two steel plates (A572, Fy = 50 ksi) are welded together to form an inverted T-beam. Determine the maximum bending stress developed. Also determine the maximum shear stress at the neutral axis of the cross-section and at the intersection where the stem joins the flange. Ignore the weight of the steel plates.

### Structural Diagram and Analysis #### Diagram Descriptions 1. **Cross-Sectional View**: - Two steel plates are shown, one measuring 1" x 8" and the other 1" x 6". - The section is welded on each side. - The centroidal axis, indicated by "N.A." (neutral axis), features dimensions that measure 5.93 inches vertically and 3.07 inches horizontally. - The moment of inertia about the x-axis (\(Ix\)) is given as 113.2 in.\(^4\). 2. **Beam Loading Diagram**: - A beam supports two concentrated loads: 5 kips (k) and 10 kips. - The beam spans 20 feet, supported at both ends (5 feet from each end). 3. **Shear Force and Bending Moment Diagrams**: - **Shear Force Diagram (V)**: - At support A, the reaction force is 6.25 kips. - The diagram progresses linearly, starting at +6.25 kips, decreasing to +1.25 kips, then down to -8.75 kips just before support B. - At support B, the reaction force is 8.75 kips. - **Bending Moment Diagram (M)**: - The moment starts at zero and increases linearly to +31.25 kip-ft at the point where the 5 kip load is applied. - Between the loads, the moment decreases linearly and reaches a maximum of +43.75 kip-ft. - The diagram returns to zero at support B. These diagrams collectively illustrate the structural behavior under given load conditions, demonstrating the bending and shear forces that influence the beam design.
Transcribed Image Text:### Structural Diagram and Analysis #### Diagram Descriptions 1. **Cross-Sectional View**: - Two steel plates are shown, one measuring 1" x 8" and the other 1" x 6". - The section is welded on each side. - The centroidal axis, indicated by "N.A." (neutral axis), features dimensions that measure 5.93 inches vertically and 3.07 inches horizontally. - The moment of inertia about the x-axis (\(Ix\)) is given as 113.2 in.\(^4\). 2. **Beam Loading Diagram**: - A beam supports two concentrated loads: 5 kips (k) and 10 kips. - The beam spans 20 feet, supported at both ends (5 feet from each end). 3. **Shear Force and Bending Moment Diagrams**: - **Shear Force Diagram (V)**: - At support A, the reaction force is 6.25 kips. - The diagram progresses linearly, starting at +6.25 kips, decreasing to +1.25 kips, then down to -8.75 kips just before support B. - At support B, the reaction force is 8.75 kips. - **Bending Moment Diagram (M)**: - The moment starts at zero and increases linearly to +31.25 kip-ft at the point where the 5 kip load is applied. - Between the loads, the moment decreases linearly and reaches a maximum of +43.75 kip-ft. - The diagram returns to zero at support B. These diagrams collectively illustrate the structural behavior under given load conditions, demonstrating the bending and shear forces that influence the beam design.
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