Lecture-01
Structural Analysis
Structural analysis is
the prediction of the performance of a given structure under prescribed loads
and/or
other external effects, such as support movements and temperature changes.
The key performance
characteristics typically assessed during structural design include:
1. Stresses
or stress resultants — such as axial forces, shear forces, and
bending moments;
2. Deflections
— the displacements or deformations of the structure;
3. Support
reactions — the forces and moments developed at the supports.
Structural Engineering
Structural engineering is
the science and art of planning, designing, and constructing safe and
economical structures that will serve their intended purposes.
Structural analysis is an integral part of any structural engineering project,
its function being the prediction of the performance of the proposed structure.
The structural
engineering process is typically iterative and consists of several
interrelated phases which generally includes:
1. Planning Phase
This initial phase
involves:
- Establishing the functional
requirements of the structure.
- Deciding on the layout, dimensions,
and structural system (e.g., frame, truss).
- Choosing materials (e.g., steel,
reinforced concrete).
- Considering non-structural factors,
such as aesthetics, cost, construction methods, and environmental impact.
This phase is critical
and requires both structural knowledge and practical experience. Its outcome is
a preliminary structural system expected to be functional and
economical.
2. Preliminary Structural Design
Here, engineers estimate member
sizes using approximate methods, past experience, and code provisions.
These preliminary sizes provide a basis for estimating self-weight and
other structural loads in the next step.
3. Estimation of Loads
This phase involves
calculating all anticipated loads on the structure, including:
- Dead loads
(self-weight),
- Live loads
(occupants, furniture),
- Environmental loads
(wind, seismic, snow, temperature).
Accurate load estimation
is vital for reliable structural analysis.
4. Structural Analysis
Using the estimated
loads, engineers perform a structural analysis to determine:
- Internal forces
(axial, shear, bending moments),
- Stresses in members,
- Deflections
of the structure.
This step forms the
analytical core of the design process and predicts how the structure will
behave under real-world conditions.
5. Safety and Serviceability Checks
The analysis results are
evaluated against applicable design codes (e.g., ACI, Eurocode, IS).
Engineers check whether the structure satisfies:
- Safety requirements
(no collapse or overstress),
- Serviceability criteria
(acceptable deflections, vibrations, and cracking).
If all criteria are met,
construction drawings and specifications can be prepared.
6. Revised Structural Design
If the structure fails to
meet code requirements, engineers revise the member sizes and repeat the
process from load estimation through analysis until compliance is achieved.
Classification of Structures
Commonly used structures
can be classified into five basic categories, depending on the type of primary
stresses that may develop in their members under major design loads.
1. Tension Structures
Tension structures
consist of members that are primarily subjected to pure tension under
external loads. These structures utilize material very efficiently, as tensile
stress is uniformly distributed over the cross-section.
Examples:
- Cable structures
used in suspension bridges and long-span roofs.
- Vertical hangers
used to suspend balconies or tanks.
- Membrane structures,
such as fabric roofs and tents (e.g., Tokyo Dome's air-supported fabric
roof).
2. Compression Structures
Compression structures
develop mainly compressive stresses under the action of external loads.
Examples:
- Columns:
Straight vertical members supporting axial loads.
- Arches:
Curved structures that act like inverted cables.
3. Trusses
Trusses are
composed of straight members connected at their ends by hinged connections to
form a stable configuration.
- Members are subjected to axial
tension or compression only (ideally).
- Lightweight and strong—commonly used
in bridges, roofs, space structures.
- Real trusses have gusset plates
with bolted/welded joints that introduce minor bending, but are usually
negligible.
4. Shear Structures
Shear structures develop in-plane
shear stresses under lateral loads (e.g., wind, earthquake).
Examples:
- Shear walls
in buildings.
5. Bending Structures
Bending structures develop
mainly bending stresses under the action of external loads. In some structures,
the shear stresses associated with the changes in bending moments may also be
significant and should be considered in their designs.
Examples:
- Beams:
Loaded perpendicularly to their longitudinal axis. Beams experience flexural
(bending) stresses—compression at the top, tension at the bottom.
- Rigid frames:
Consist of beams and columns connected rigidly. Rigid frames resist bending,
shear, and axial forces.
- Slabs and plates:
Common in floor and roof systems.
Plane vs. Space Structures
Structural systems can be
classified based on their geometry and the way they carry loads. One
fundamental classification is into plane structures and space
structures. Understanding this distinction is crucial for choosing the
appropriate analytical methods and design approaches.
ü Plane
structures are composed of members that lie entirely within a single plane
(typically the x-y plane) and are subjected to loads that also act in that same
plane.
ü Space
structures are three-dimensional systems with members and loads acting
in multiple directions, typically along the x, y, and z axes.
Loads on Structures
·
Dead Loads
·
Live Loads
·
Wind Loads
·
Snow Loads
·
Earthquake Loads
·
Hydrostatic and Soil Pressures
·
Thermal and Other Effects
Structural Systems for Transmitting Loads
Floor Systems and Tributary Areas
The floor and roof slabs
of multistory buildings, and the deck slabs of bridges, are often supported on
rectangular grids of beams and girders called floor systems.
During the design
process, an engineer needs to determine how much of the total distributed load
applied over the area of the slab is carried by each member (i.e., a beam, a
girder, or a column) of the floor system. The portion of the slab area whose
load is carried by a particular member is called the tributary area of
the member.
Figures (a) and (b)
illustrate the tributary areas of the edge beams supporting square and
rectangular two-way slabs, respectively. These figures also show the loads
carried by edge beams due to a uniformly distributed pressure w (force
per unit area) applied to the surface area of the slab.
