Slope Deflection Method in Structural Analysis

Slope Deflection Method

• A structural analysis method for determining the moments and rotations at the ends of beams and frames.
• Focuses on the relationship between slope and deflection at each joint of the structure.
• Applicable for both continuous beams and portal frames.

Continuous Beams

• Analysis of continuous beams:
  • Involves solving a system of equations representing the equilibrium conditions for each joint.
  • Takes into account the support conditions, including fixed ends, pinned ends, and roller supports.
  • Incorporates the stiffness of individual members and the relative stiffness of the supports.
  • Considers the influence of support settlement on the internal moments and shear forces.
• Sinking of support:
  • Causes additional moments and forces in the structure.
  • Affects the distribution of loads and stress in the beam.
  • Can create significant stresses in the beam, particularly in the vicinity of the sinking support.
  • The magnitude of the moments and forces due to sinking depends on the amount of settlement and the relative stiffness of the members.
• Without sinking of support:
  • Simpler analysis as the only loads are gravity loads.
  • Still uses the slope deflection method to solve for the unknown moments and slopes at each support.

Portal Frames Without Side Sway

• Frames are assumed to be rigid, with rigid joints, and the assumption is made that the frame is perfectly rigid.
• Analysis of portal frames:
  • Similar to continuous beams, but also considering the horizontal and vertical forces at the joints.
  • Involves solving a system of equations that accounts for the equilibrium of both forces and moments at the frame joints.
  • The slope deflection method considers the stiffness of individual members and the relative stiffness of the supports.
• Without side sway:
  • Simplified analysis because the frame is assumed not to move horizontally.
  • It eliminates the need to consider horizontal forces and moments, which can simplify the calculations.
  • Only gravity loads are considered.
  • However, it is important to note that the assumption of no side sway may not always be valid, especially for frames subjected to lateral loads.

This quiz explores the Slope Deflection Method, a crucial technique in structural analysis used for determining moments and rotations in beams and frames. It covers continuous beams and the effects of support conditions, including sinking supports. Test your knowledge on the relationships between slope, deflection, and structural integrity.