ES3 PRELIMS

Roller, Rocker, Link, Hinge, Fixed

What are the different types of supports in a structural system?

Support Reaction

The opposing forces or reactions exerted by structural supports to counter the effects of applied loads on a structural element/member.

1

How many unknowns are there in the reaction force for a roller support?

Roller Support

A type of support that allows vertical movement but prevents horizontal movement of a structural element/member.

The magnitude of Rx and Ry (the rectangular components)

What is the unknown in the reaction force for a fixed support?

Fixed Support

A type of support that prevents both vertical and horizontal movement of a structural element/member.

The magnitudes of Ry, Rz, and M (the three unknowns)

What is the unknown in the reaction force for a hinge support?

Hinge Support

A type of support that allows rotation of a structural element/member around a fixed axis while preventing translation in any direction

By exerting opposing forces or reactions to counter the effects of applied loads on a structural element/member.

How do structural supports maintain equilibrium?

Statically Determinate Structures

Structures in which all the forces can be determined strictly from the equations of static equilibrium.

Rocker

What is the symbolic representation for a roller support?

Fx = 0, Fy = Ry, M = 0

What are the reactions for a roller support?

Statically determinate structures

Structures in which all the forces can be determined strictly from the 3 equations of static equilibrium

Degree of indeterminacy

The number of unknown reactions in a structure minus the number of equations of equilibrium and conditions

Check if the number of reactions is greater than or equal to the number of equilibrium and condition equations, and if the reactions are not parallel or concurrent.

How do you determine if a beam is stable or unstable?

Shear and moment diagram

A graphical representation of the shear and bending forces on a beam due to applied loads

Pass sections where there are significant changes in loading and calculate the moment by summing the moment of forces at that section.

How do you construct a moment diagram?

Resultant of line loads

An equivalent concentrated load that represents the line load on a beam

Stability of beams

Refers to whether a beam is stable or unstable, and whether it is determinate or indeterminate in terms of its reactions.

Hinge support

What is the term for the type of support that can rotate and translate?

Reactions

Opposing forces or reactions exerted by supports to maintain equilibrium in a structural system

3 unknowns

How many unknowns are there for a fixed support connection?

1

What is the number of reactions for a beam supported by a pin connection?

Statically determinate structure

A structure where all the forces can be determined strictly from the equations of static equilibrium

3 equilibrium equations

How many equilibrium equations are required for a statically determinate beam?

Degree of indeterminacy

The number of unknowns minus the number of equilibrium equations for a structure

The number of reactions must be greater than or equal to the number of equilibrium equations, reactions must not be parallel, and reactions must not be concurrent.

What are the conditions for beam stability?

Shear and moment diagram

A graphical representation of the shear and bending forces in a beam due to applied loads.

Static Equilibrium

The condition in which all forces and moments acting on a body are balanced and the body is at rest or moving at a constant velocity.

The ability to determine all forces in the structure using the 3 equations of static equilibrium.

What determines whether a structure is statically determinate or indeterminate?

By plotting the corresponding shearing force at different sections along the beam.

How do you construct a shear diagram for a beam?

Beam

A slender structural member designed to support loads applied at various points perpendicular to their longitudinal axis.

DI

Degree of Indeterminacy

R

Number of Reactions

C

Number of Releases (Equations of Conditions)

Internal Hinge

A type of support condition for a beam where the beam allows rotation at a specific point.

Line Load

A load applied continuously along a linear segment of a beam.

Beam Stability

A structure is statically stable if the following conditions are met: 1) The number of reactions must be greater than or equal to the number of equilibrium equations and equations of condition (R≥3+C), 2) All reaction forces must not be parallel to each other, 3) All support reactions must not be concurrent.

Beam Determinacy

he formula DI = R - 3 - C, where DI is the degree of indeterminacy, R is the number of reactions, and C is the number of releases (equations of condition).

Simply Supported Beam

A beam supported at both ends with no additional support in between.

Cantilever Beam

A beam supported at one end with no support at the other end.

Overhanging Beam

A beam with one or both ends extending beyond its supports.

Propped Beam

A beam supported at one or more points along its length.

Continuous Beam

A beam supported over three or more supports.

1. The number of reactions must be greater than or equal to the number of equilibrium equations and equations of condition (R ≥ 3 + C).

What conditions must be met for a structure to be statically stable?