engineers began applying the knowledge of mechanics in designing structures Mechanics → mathematics and science

➢ the prediction of the performance of a given structure under prescribed loads and/or other external effects, such as support movements and temperature changes

originator of the theory of structures

developed the law of linear relationships between the force and deformation of materials

➢ formulated the laws of motion and developed calculus

formulated the principle of virtual work

developed the theory of buckling of columns

presented the analysis of bending of elastic beams

published a treatise on elastic behavior of structures in 1826

formulated the three-moment equation for the analysis of continuous beams

presented the method of consistent deformations and the law of reciprocal deflections

developed the conjugate-beam method for calculation of deflections and Mohr’s circles of stress and strain

formulated the theorem of least work

developed the moment-area method

presented a principle for constructing influence lines

developed the slope-deflection method slope-deflection method → precursor of the matrix stiffness method

developed the moment-distribution method in 1924

revolutionized structural analysis

the science and art of planning, designing, and constructing safe and economical structures that will serve their intended purposes

➢ integral part of any structural engineering project ➢ prediction of the performance of the proposed structure

involves the establishment of the functional requirements of the proposed structure, the general layout and dimensions of the structure, consideration of the possible types of structures that may be feasible and the types of materials to be used ➢ perhaps the most crucial phase of the entire project and requires experience and knowledge of construction practices in addition to a thorough understanding of the behavior of structures

sizes of the various members of the structural system selected in the planning phase are estimated based on approximate analysis, past experience, and code requirements

involves determination of all loads that can be expected to act on the structure

values of the loads are used to carry out an analysis of the structure in order to determine the stresses or stress resultants in the members and the deflections at various points of the structure

results of the analysis are used to determine whether or not the structure satisfies the safety and serviceability requirements of the design code

if the code requirements are not satisfied, then the member sizes are revised, and phases 3 through 5 are repeated until all the safety and serviceability requirements are satisfied

subjected to pure tension under the action of external loads ➢ composed of flexible steel cables, vertical rods used as hangers, membrane structures such as tents ➢ support bridges and long-span roofs

develop mainly compressive stresses under the action of external loads ➢ columns and arches columns – straight members subjected to axially compressive loads beam – column → when subjected also to lateral loads and/or moments arch – a curved structure, with a shape similar to that of an inverted cable ➢ susceptible to buckling or instability → adequate bracing must be provided

composed of straight members connected at their ends by hinged connections to form a stable configuration loaded only at the joints ➢ members either elongate or shorten ➢ support roofs of buildings

used in multistory buildings to reduce lateral movements due to wind loads and earthquake excitations ➢ example is reinforced concrete shear walls

develop mainly bending stresses under the action of external loads ➢ commonly used are beams, rigid frames, slabs, and plates beam ▪ a straight member that is loaded perpendicular to its longitudinal axis rigid frames ▪ composed of straight members connected together either by rigid (moment-resisting) connections or by hinged connections to form stable configurations ▪ can be loaded on the members as well as on the joints ▪ members are subjected to bending moment, shear, and axial compression or tension under the action of external loads ▪ multistory buildings, bridges, industrial plants

simplified representation, or an ideal, of a real structure for the purpose of analysis

three-dimensional structures can be subdivided into plane structures for analysis plane structure ▪ all the members of a structure as well as the applied loads lie in a single plane

representation of analytical model of a body selected for analysis

used to join members of structures a. Rigid connection ▪ prevents relative translations and rotations of the member ends connected to it ▪ all member ends connected to a rigid joint have the same translation and rotation b. hinged connection prevents only relative translations of member ends connected to it ▪ all member ends connected to a hinged joint have the same translation but may have different rotations

do not allow any movement

can prevent translation but permit rotation

can prevent translation in only one direction