In Section 3.4, we indicated that the types of connections used to connect rigid portions of internally unstable structures provide equations of condition that, along with the three equilibrium equations, can be used to determine the reactions needed to constrain such structures fully. Three types of connection arrangements commonly used to connect two rigid trusses to form a single (internally

### Arrangement of Members of Plane Trusses-Internal Stability

Based on our discussion in Section 3.4, we can define a plane truss as internally stable if the number and geometric arrangement of its members is such that the truss does not change its shape and remains a rigid body when detached from the supports. The term internal is used here to refer to the number and arrangement of members

### Assumptions for Analysis of Trusses

The analysis of trusses is usually based on the following simplifying assumptions: 1. All members are connected only at their ends by frictionless hinges in plane trusses and by frictionless ball-and-socket joints in space trusses. 2. All loads and support reactions are applied only at the joints. 3. The centroidal axis of each member coincides with the line connecting the

### Equilibrium and Support Reactions

3.1 Equilibrium of Structures 3.2 External and Internal Forces 3.3 Types of Supports for Plane Structures 3.4 Static Determinacy, Indeterminacy, and Instability 3.5 Computation of Reactions 3.5.1 Computation of Reactions Problems and Solutions 3.6 Principle of Superposition 3.7 Reactions of Simply Supported Structures Using Proportions The objective of this chapter is to review the basic concept of equilibrium of structures

### Reactions of Simply Supported Structures Using Proportions

Consider a simply supported beam subjected to a vertical concentrated load P, as shown in Fig. 3.26. By applying the moment equilibrium equations, ∑MB =0 and ∑MA =0, we obtain the expressions for the vertical reactions at supports A and B, respectively, as where, as shown in Fig. 3.26, a = distance of the load P from support A (measured

### Principle of Superposition

The principle of superposition simply states that on a linear elastic structure, the combined efect of several loads acting simultaneously is equal to the algebraic sum of the e¤ects of each load acting individually. For example, this principle implies, for the beam of Example 2, that the total reactions due to the two loads acting simultaneously could have been obtained

### Computation of Reactions Problems and Solutions

Determine the reactions at the supports for the frame shown in Fig. 3.20(a). Solution Free-Body Diagram See Fig. 3.20(b). Static Determinacy The frame is internally stable with r =3. Therefore, it is statically determinate. Support Reactions Example 3.7 Determine the reactions at the supports for the beam shown in Fig. 3.21(a). Solution Free-Body Diagram See Fig. 3.21(b). Static Determinacy The

### Computation of Reactions

The following step-by-step procedure can be used to determine the reactions of plane statically determinate structures subjected to coplanar loads. 1. Draw a free-body diagram (FBD) of the structure. a. Show the structure under consideration detached from its supports and disconnected from all other bodies to which it may be connected. b. Show each known force or couple on the

### Static Determinacy, Indeterminacy, and Instability

Internal Stability A structure is considered to be internally stable, or rigid, if it maintains its shape and remains a rigid body when detached from the supports. Conversely, a structure is termed internally unstable (or nonrigid) if it cannot maintain its shape and may undergo large displacements under small disturbances when not supported externally. Some examples of internally stable structures

### Types of Supports for Plane Structures

Supports are used to attach structures to the ground or other bodies, thereby restricting their movements under the action of applied loads. The loads tend to move the structures; but supports prevent the movements by exerting opposing forces, or reactions, to neutralize the e¤ects of loads, thereby keeping the structures in equilibrium. The type of reaction a support exerts on