CE 411 - Lecture Notes

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THEORY OF STRUCTURES (Lecture Notes) INTRODUCTION TO STRUCTURAL ANALYSIS Structural Analysis – the prediction of the performance of a given structure under prescribed loads and/ or other external effects, such as support movements and temperature changes. Galileo Galilei (1564 - 1642) – generally considered to be the originator of the theory of structures. Role of Structural Analysis in Structural Engineering Projects Structural Engineering – the science and art of planning, designing and constructing safe and economical structures that will serve their intended purposes.

Figure 1: Phase of a Typical Structural Engineering Project

1. Planning Phase – this phase usually 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 (e.g. rigid frame or truss) that may be feasible and the types of materials to be used (e.g. structural steel, timber or reinforced concrete) 2. Preliminary Structural Design – in this phase, the 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. 3. Estimation of Loads – it involves determination of all the loads that can be expected to act on the structure. 4. Structural Analysis – the values of the loads are used to carry out an analysis of the structure in order to determine the stresses or stress results in the members and the deflections at various points of the structure. 5. Safety and serviceability checks – the results of the analysis are used to determine whether or not the structure satisfies the safety and serviceability requirements of the design codes. 6. Revised Structural Design – 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. Prepared by: Engr. John Le Carre A. Enerlan, CIT University, CEA-CE_1401 Source: Understanding Structural Analysis by Aslam Kassimali, Philippine Edition

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Classification of Structures 1. Tension Structures – the members of tension structures are subjected to pure tension under the action of external loads. - Examples: Cables (Suspension Bridge) and Hangers

loading conditions Figure2:1:Single Single cable cable under Figure undertwo twodifferent different loading conditions

Figure 3: Suspension Bridge

2. Compression Structures – these structures develop mainly compressive stresses under the action of external loads. - Examples: Columns and Arches * Columns – are straight members subjected to axially compressive loads. When a straight member is subjected to lateral loads and/ or moment in addition to axial loads it is called a beam – column.

Figure 4: Column Prepared by: Engr. John Le Carre A. Enerlan, CIT University, CEA-CE_1401 Source: Understanding Structural Analysis by Aslam Kassimali, Philippine Edition

Figure 5: Arch

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3. Trusses – are composed of straight members connected at their ends by hinged connections to form a stable configuration. - Examples: Roof Truss and Bridge Truss

Figure 6: Plane Truss

4. Shear Structure – are used in multistory buildings to reduce lateral movements due to wind loads and earthquake excitations. - Example: Shear Wall

Figure 7: Shear Wall

5. Bending Structure – these structures develop mainly bending stresses under the action of external loads. - Examples: Beams and Rigid Frames * Beams – is a straight member that is loaded perpendicular to its longitudinal axis.

Figure 8: Beam

* Rigid Frames – are composed of straight members connected together either by rigid (moment-resisting) connections or by hinged connections to from stable configurations.

Figure 9: Rigid Frames Prepared by: Engr. John Le Carre A. Enerlan, CIT University, CEA-CE_1401 Source: Understanding Structural Analysis by Aslam Kassimali, Philippine Edition

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Plane Structures – if all the members of a structure as well as the applied loads lie in a single plane. Space Structures – are analyzed as three-dimensional bodies subjected to three-dimensional force systems. Line Diagram – the analytical model of the two- or three-dimensional body selected for analysis on this diagram, each member of the structure is represented by a line coinciding with it centroidal axis. Connections – are commonly used to join members of structures. Two types of Connection: 1. Rigid Connection – a connection or joint prevents relative translations and rotations of the member ends connected to it; that is, all member ends connected to a rigid joint have the same translation and rotation. 2. Flexible, or Hinged Connection – a connection or joint prevents only relative translations of member ends connected to it; that is, all member ends connected to a hinged joint have the same translation but may have different rotations. Supports – supports for plane structures are commonly idealized as either fixed supports, which do not allow any movement; hinged supports, which can prevent translation but permit rotation; or roller, or link supports, which can prevent translation in only one direction.

Figure 10: Framing of a Bridge

Prepared by: Engr. John Le Carre A. Enerlan, CIT University, CEA-CE_1401 Source: Understanding Structural Analysis by Aslam Kassimali, Philippine Edition

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Figure 11: Framing of a Multistory Building

LOADS ON STRUCUTURES Types of Load 1. Dead Loads 2. Live Loads 3. Wind Loads 4. Earthquake Loads Dead Load - are gravity loads of constant magnitudes and fixed positions that act permanently on the structure. Such loads consist of the weights of the structural system itself and of all other material and equipment permanently attached to the structural system. For example, the dead loads for a building structure include the weights of frames, framing and bracing systems, floors, roofs, ceilings, walls, stairways, heating and air-conditioning systems, plumbing, electrical systems, and so forth. Table 1: Unit Weights of Some Common Construction Materials

Prepared by: Engr. John Le Carre A. Enerlan, CIT University, CEA-CE_1401 Source: Understanding Structural Analysis by Aslam Kassimali, Philippine Edition

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Live Load - are loads of varying magnitudes and/or positions caused by the use of the structure. The codes use the term live loads to refer only to those variable loads caused by the use of the structure. The magnitudes of design live loads are usually specified in building codes. Wind Load - are produced by the flow of wind around the structure. The magnitudes of wind loads that may act on a structure depend on the geographical location of the structure, obstructions in its surrounding terrain, such as nearby buildings, and the geometry and the vibrational characteristics of the structure itself. Earthquake Load – derived from the sudden undulation of a portion of the earth’s surface, earthquake. Tributary Area (TA) – is the loaded area of a particular structure that directly contributes to the load applied to a particular member in the structure. It is best defined as the area bounded by lines halfway to the next beam or to the next column.

Figure 12: Sample Floor Framing Plan

Prepared by: Engr. John Le Carre A. Enerlan, CIT University, CEA-CE_1401 Source: Understanding Structural Analysis by Aslam Kassimali, Philippine Edition