Simply Supported Beam

Definition

A simply supported beam is a type of structural member that is supported at both ends, allowing it to freely rotate and translate without any moment resistance at the supports. This basic configuration is crucial in analyzing how loads affect the beam, as it simplifies calculations for shear forces, bending moments, normal stresses, shear stresses, combined loading scenarios, and deflection.

5 Must Know Facts For Your Next Test

1. Simply supported beams can have various loading conditions, including point loads and distributed loads, which influence their shear and moment diagrams.
2. At the supports of a simply supported beam, there are no moments; therefore, the reactions at the supports can be calculated using static equilibrium equations.
3. The maximum bending moment in a simply supported beam occurs at the location where shear force changes sign, typically under point loads or at mid-span for uniformly distributed loads.
4. Shear stress distribution in a simply supported beam varies across its depth, being highest at the neutral axis and decreasing towards the outer fibers.
5. To determine deflection in a simply supported beam, methods such as the double integration method or the use of tables for standard loading cases can be employed.

Review Questions

• How does the support condition of a simply supported beam influence its bending moment and shear force diagrams?
  • The support condition of a simply supported beam allows it to freely rotate and translate at its ends, which directly affects its bending moment and shear force diagrams. The absence of moment resistance at the supports leads to specific patterns where shear forces are greatest near point loads and decrease towards zero at the supports. This results in characteristic shapes for both diagrams: bending moments typically peak between loads and shear forces exhibit linear or piecewise linear trends based on load distribution.
• Discuss the significance of normal stress in simply supported beams and how it relates to applied loading conditions.
  • Normal stress in simply supported beams arises due to bending moments generated by applied loads. As the beam bends, different fibers experience tension or compression depending on their position relative to the neutral axis. The magnitude of normal stress is determined by the bending moment at any section, calculated using the formula $$ ext{Normal Stress} = rac{M imes c}{I}$$ where M is the moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia. Understanding this relationship is crucial for ensuring that beams do not exceed allowable stress limits under service conditions.
• Evaluate how combined loading affects a simply supported beam's overall performance and safety under various loading scenarios.
  • Combined loading introduces additional complexities to a simply supported beam's analysis by simultaneously applying axial loads, bending moments, and shear forces. These combinations can lead to interactions that amplify stress concentrations in critical areas. To assess overall performance and safety, engineers must consider combined stresses using principles such as the superposition method or Mohr's Circle for stress transformation. This thorough evaluation helps ensure that the beam can safely carry its intended loads without failing due to excessive normal or shear stresses resulting from unexpected loading conditions.

Related terms

Bending Moment: The internal moment that causes a beam to bend; it is influenced by the external loads and the beam's support conditions.

Shear Force: The internal force acting along the cross-section of a beam that results from external loads, causing sliding between adjacent sections.

Deflection: The displacement of a beam from its original position due to applied loads; it is important for ensuring structural integrity and serviceability.