To develop the ability to model or idealize a structure so that the structural engineer can perform a practical force analysis of the members
*Support Connections
- Pin connection (allows some freedom for slight rotation)
- Roller support (allows some freedom for slight rotation)
- Fixed joint (allows no relative rotation)
- E.g. are shown in Fig 2.1 & 2.2
- Idealized models used in structural analysis are shown in Fig 2.3
Fig 2.1 & 2.2 & 2.3
Fig 2.1 & 2.2 & 2.3
Fig 2.1 & 2.2 & 2.3
*Support Connections
- In reality, all connections exhibit some stiffness toward joint rotations owing to
friction & material behavior
- A more appropriate model for a support or joint might be that shown in Fig 2.3 (c)
- If k = 0 the joint is pin and -> , the joint is fixed
- When selecting the model for each support, the engineer must be aware how the
assumptions will affect the actual performance
- The assumptions must be reasonable for the structural design
- The analysis of the loadings should give results that closely approximate the
actual loadings
- Common types of connections on coplanar structures are given in Table 2.1
- In reality, all supports actually exert distributed surface loads on their
contacting members
- The concentrated forces & moments shown in Table 2.1 represents the resultants of
these loads distributions
Table 2.1
*Idealized Structure
- Consider the jib crane & trolley in Fig 2.5(a)
- For analysis, we neglect the thickness of the 2 main member & will assume that the
joint at B is fabricated to be rigid
- The support at A can be modeled as a fixed support
- Details of trolley can be excluded
- The members of the idealized structure is shown in Fig 2.5(b)
Idealized Structure
Fig 2.5
Idealized Structure
Consider the framing used to support a typical floor slab in a building as shown in Fig 2.6(a)
The slab is supported by floor joists located at even intervals
These are in turn supported by 2 side girders AB & CD
Loads
*Highway Bridge loads
- Primary live loads are those due to traffic
- Specifications for truck loadings are reported in AASHTO
- For 2-axle truck, these loads are designated with H followed by the weight of
truck in tons and another no. gives the year of the specifications that the load
was reported
*Railway Bridge loads
- Loadings are specified in AREA
- A modern train having a 320kN (72k) loading on the driving axle of the engine is
designated as an E-72 loading
- The entire E-72 loading for design is distributed as shown in Fig 1.11
*Impact loads
- Due to moving vehicles
- The % increase of the live loads due to impact is called the impact factor, I
- From AASHTO
*Wind loads
- Kinetic energy of the wind is converted into potential energy of pressure when
structures block the flow of wind
- Effects of wind depends on density & flow of air, angle of incidence, shape &
stiffness of the structure & roughness of surface
- For design, wind loadings can be treated as static or dynamic approach
*Wind loads
- For static approach
*Wind loads
- Once qz is obtained, the design pressure can be obtained from a list of relevant
eqns
*Wind loads
*Wind loads
- Applications of eqn 1.3 will involve calculations of wind pressures from each
side of the building with due considerations for the possibility of either
positive or negative pressures acting on the building’s interior
- For high-rise building or those having as shape or location that makes them wind
sensitive, it is recommended that a dynamic approach is used
Example
*The enclosed building shown in Fig 1.4a is used for agricultural purposes and is
located outside of Chicago, Illinois on flat terrain
*When the wind is directed as shown, determine the design wind pressure acting on
the roof and sides of the building using the ASCE 7-02 specifications
*Fig 1.14
solution
Fig 1.14(c)
*Wind loads
- If the structure represents an above-ground sign, the wind will produce a
resultant force on the face of the sign which is determined from:
*Wind loads
*Snow loads
- Design loadings depend on building’s general shape & roof geometry, wind
exposure,location and its importance
- Snow loads are determined from a zone map reporting 50-year recurrence interval
- For flat roof (slope < 5%):
Example
*The unheated storage facility shown in Fig 1.15 is located on flat open terrain
near Cario, Illinois where the ground snow load is 0.72kN/m2
*Determine the design snow load on the roof
Fig 1.15
*Earthquake loads
- Earthquake produce loadings through its interaction with the ground & its
response characteristics
- Their magnitude depends on amount & type of ground accel, mass & stiffness of
structure
- To illustrate, consider Fig 1.16
- This model may represent a single-story building
- The top block is the lumped mass of the roof
- The middle block is the lumped stiffness of all the building’s columns
- During earthquake, the ground vibrates both horizontally & vertically
- Horizontal accel -> shear forces in the column
- If the column is stiff & the block has a small mass, the period of vibration of
the block will be short, the block will accel with the same motion as the ground
& undergo slight relative displacements
- If the column is very flexible & the block has a large mass, induced motion will
cause small accelerations of the block & large relative displacement
- Fig 1.16
- The effects of a structure’s response can be determined & represented as an
earthquake response spectrum
-For small structure, static analysis is satisfactory
*Hydrostatic & Soil Pressure
- The pressure developed by these loadings when the structures are used to retain
water or soil or granular materials
- E.g. tanks, dams, ships, bulkheads & retaining walls
*Other natural loads
- Effect of blast
- Temperature changes
- Differential settlement of foundation
Structural Design
*Material uncertainties occur due to
- variability in material properties
- residual stress in materials
- intended measurements being different from fabricated sizes
- material corrosion or decay
*Many types of loads discussed previously can occur simultaneously on a structure
*However, it is unlikely that the max of all these loads will occur at the same time
*In working-stress design, the computed elastic stress in the material must not
exceed the allowable stress along with the following typical load combinations as
specified by the ASCE 7-02 Standard
- Dead load
- 0.6 (dead load) + wind load
- 0.6 (dead load) + 0.7(earthquake load)
*Ultimate strength design is based on designing the ultimate strength of critical
sections
*This method uses load factors to the loads or combination of loads
- 1.4 (Dead load)
- 1.2 (dead load) + 1.6 (live load) + 0.5 (snow load)
- 1.2 (dead load) + 1.5(earthquake load)+ 0.5 (live load)
Introduction
*Structures refer to a system of connected parts used to support a load
*Factors to consider
- Safety
- Esthetics
- Serviceability
- Economic & environmental constraints
Classification of Structures
*Structural elements
- Tie rods
- Beams
- Columns
*Types of structures
- Trusses
- Cables & Arches
- Surface Structures
Loads
*Design loading for a structure is often specified in codes
- General building codes
- Design codes
*Table 1.1 lists some of the important codes used in practice
*Types of load
- Dead loads
> Weights of various structural members
> Weights of any objects that are permanently attached to the structure
> The densities of typical building materials are listed in Table 1.2 & 1.3
Example
*The floor beam in Fig 1.8 is used to support the 1.83m width of lightweight plain
concrete slab having a thickness of 102mm
*The slab serves as a portion of the ceiling for the floor below & its bottom coated
with plaster
*A 2.44m high, 305mm thick lightweight solid concrete block wall is directly over the
top flange of the beam
*Determine the loading on the beam measured per m length of the beam
Example
Solution
Using the data in Table 1.2 & 1.3:
Loads
*Live loads
- Varies in magnitude & location
- Building loads
> Depends on the purpose for which the building is designed
> These loadings are generally tabulated in local, state or national code
> A sample is shown in Table 1.4
Table 1.4
*Live loads
- Building Loads
> Uniform, concentrated loads
> For buildings having very large floor areas, many codes allow a reduction in
the uniform live load for a floor as it is unlikely the prescribed live load
will occur simultaneously
> ASCE 7-02 allows a reduction of live load on a member having an influence area
(KLL AT) of 37.2 m2 or more
*Live loads
- Building Loads
Example
* A 2-storey office building has interior columns that are spaced 6.71m apart in 2
perpendicular directions (see Fig 1.9)
* If the (flat) roof loading is 0.96kN/m2, determine the reduced live load supported
by a typical interior column located at ground level
Fig 1.9
From Fig 1.9,
