Mechanical Engineering: Trusses, Bridges & Other Structures (34 of 34) Forces=? on Members (Section) By Michel van Biezen
Summary:
Introduction: The video introduces the method of sections to solve a bridge example previously discussed.
Bridge Structure: The bridge discussed is 50 meters long with a height determined by the tangent of an angle (θ) at 7.269 meters.
Cutting Sections: Sections are made by cutting the bridge at specific points, allowing for analysis of forces on individual segments.
Forces in Sections: Sections enable the determination of forces (e.g., SBC, CE, SDE, CD) on the bridge segments.
Upper Section Analysis: Starting with the upper section, forces are calculated by summing moments around pivot points.
Moment Calculation: Moments are calculated for each force using the perpendicular distance from the pivot point.
Solving for FDE: The force FDE is calculated to be 8,660 Newtons using the method of sections.
Confirmation of Results: The value obtained matches that from a previous video, confirming the accuracy of the method.
Analysis of FCD: FCD is calculated next by summing moments around a different pivot point.
Direction Consideration: The direction of forces is considered, noting that compression forces yield negative values in the calculations.
Calculation Process: The calculation involves distances and angles to find the force FCD, resulting in a value of -10,000 Newtons.
Lower Section Analysis: Moving to the remaining section of the bridge, forces on the remaining segments are analyzed.
Analysis of FBC: Forces on the segment BC are determined by summing moments around a pivot point.
Moment Calculation: Moments are calculated for the known and unknown forces, with attention paid to their directions.
Solving for FBC: The force FBC is calculated to be -17,320 Newtons, indicating compression in the segment.
Analysis of FCE: Finally, FCE is calculated using moments around another pivot point.
Moment Calculation: Moments are calculated considering the forces and their distances from the pivot point.
Solving for FCE: FCE is calculated to be 10,000 Newtons, indicating tension in the segment.
Summary: The video concludes by confirming the calculated forces on each segment of the bridge using the method of sections.
Overall, the method of sections is demonstrated as an effective technique for analyzing forces in bridge structures.