I L D for Simply Supported Beam - Rolling Loads and Influence Line Diagrams - Structural analysis 1

TL;DR

Learn how to calculate influence line diagrams for support reactions, shear force, and moment in a simply supported beam.

Transcript

hello students so now we are going to start uh with a problem on simply supported beam okay so we'll draw influence line diagram for simply supported beam here is a simply supported beam okay so you can see a simply supported beam on which uh one support is hinged and one is roller support right now such beam is given now we need to uh draw influen... Read More

Key Insights

• 😁 Drawing influence line diagrams for support reactions, shear force, and moment in a simply supported beam involves considering the summation of forces and moment equations.
• 👈 The equations for influence line diagrams show a linear variation with respect to the distance x and the reference point Z.
• 🇦🇪 Support reactions can be calculated by assuming a unit load at a certain distance from the support and analyzing the equilibrium conditions.
• 😁 Influence line diagrams provide a graphical representation of how support reactions, shear force, and moment vary with the position of a unit load along the beam.

Questions & Answers

Q: How do you calculate influence line diagrams for support reactions in a simply supported beam?

To calculate the influence line diagram for support reactions, we consider the summation of forces in the y-direction and the moment about one support. By assuming a unit load acting at a distance x from the support, we can derive an equation that shows a linear variation of support reaction with x.

Q: What is the equation for the influence line diagram of support reaction at point A?

The equation for the influence line diagram of support reaction at point A is: R_A = 1 - (x/l), where R_A represents the support reaction at A and l is the total span of the beam. This equation shows a linear variation of support reaction with x.

Q: How do you calculate the influence line diagram for shear force at point C?

The calculation of the influence line diagram for shear force at point C involves considering two cases. When x is less than the distance between the support and C (z), the shear force is given by -x/l. When x is greater than z, the shear force is equal to 1 - z/l.

Q: How do you determine the influence line diagram for the moment at point C in a simply supported beam?

The influence line diagram for the moment at point C is calculated by considering the moment about C. When x is less than z, the moment is given by -zx/l + x. When x is greater than z, the moment is equal to z(l - z)/l.

Summary & Key Takeaways

• This content provides a step-by-step guide on drawing influence line diagrams for support reactions, shear force, and moment in a simply supported beam.

• The process involves calculating support reactions using the summation of forces and moment equations.

• Influence line diagrams are plotted by substituting values of x (distance) and Z (reference point) into the equations.