Beam Reaction Calculation Quiz

Force Method of Analysis

• In the force method of analysis, typically only 3 equilibrium equations are available for solution.
• A beam with additional unknowns to solve is referred to as a "redundant" beam.

Redundant Support Reaction

• When a support reaction is chosen as 'redundant,' the external load's effect is temporarily removed from the beam.

Additional Equation

• An additional equation is necessary for solution in the force method of analysis because the available equilibrium equations are not enough to determine the unknowns.

Method of Analysis

• The method that uses coefficients of the unknowns and stiffness coefficients for analysis is the force method.
• The key principle involved in obtaining the additional equation needed for solution in the force method of analysis is the compatibility of deformations.

Beam Properties

• The width of the beam is not specified in the text.
• If E = 200 GPa, the value of E in MPa is 200,000 MPa.

Problem-Specific Details

• In problem 9–11, points A and B have fixed and simple supports, respectively.
• In problem 9–16, the joints at points A and C are assumed to be rigid.
• In problem 9–14, after determining the reactions at the supports, the deflection and slope of the beam need to be found.
• In all problems mentioned in the text, the material properties of the beam and rod are constant.

Beam Deflection

• The moment of inertia of the beam AB is not specified in the text.
• If the temperature of the rod decreases by 80°C, a compressive force is developed in the rod.

Support Types

• Point A is a fixed support.
• The beam and rod are made of a material with a modulus of elasticity (E) of 200 GPa.

Primary Purpose

• The primary purpose of using the force method of analysis in structural engineering is to analyze indeterminate beams.

Influence Line

• The principle used to sketch the influence line for the moment at D is the Muller-Breslau principle.

Compatibility Equations

• In the context of Fig. 9–6, compatibility equations are necessary for solving the beam deflection because they relate the deformations of the beam to the redundants.
• EI represents the flexural rigidity of the beam.

Redundants

• Redundants By and Cy play a role in the force method of analysis for indeterminate beams, as they help to find the additional equation needed for solution.

Flexibility Coefficients

• The action that helps in determining the flexibility coefficients fCC and fBC in the force method of analysis is the application of a unit load.

Superposition

• Superposition aids in solving problems related to beam deflection analysis by allowing the combination of individual effects to find the total effect.

Equation Analysis

• The equation $0 = -9000 + \frac{576}{EI}$ can be inferred to be related to the beam deflection analysis.
• The equation $0.04 = \frac{\triangle B}{EI} + ByfBB$ represents the compatibility equation for the beam deflection.

Moment Diagram

• The purpose of determining all reactions before constructing the moment diagram is to find the correct moment values.
• The center support B is chosen as the redundant in the analysis because it allows for the creation of a determinate beam.

Indeterminate Beam

• The significance of having a beam indeterminate to the first degree is that it requires the use of the force method of analysis to find the additional equation needed for solution.