Chapter Two Loads

Theory of structure one: Lecture notes on Loads on structures Page 1

Chapter two: Loads on structures

Introduction

It is necessary to determine the loads the structure must support. So once the dimensions of the structure

are defined, the actual design begins with those elements that are subjected to the primary loads the

structure is intended to carry and proceeds in sequence to the various supporting members until the

foundation is reached. Thus a building floor slab would be designed first followed by the supporting beams,

columns, and last the foundation footings. In order to design a structure, it is therefore necessary to first

specify the loads that act on it. The design load for a structure is often specified in codes. Ethiopian

Building Code Standards one(EBCS-1) gives details of the loading on structures.

2.1. Dead loads

Dead loads consists of the weights of the various structural members and the weights of any objects that

are permanently attached to the structure. Hence for building, the dead loads include the weights of

columns, beams, and girders and floor slabs, roofing, walls, windows, plumbing, electrical fixtures and

other miscellaneous attachments. For a highway bridge, the dead load consists of the main supporting

trusses or girders, the floor beams and stringers of the floor system, the roadway slabs, the curbs,

sidewalks, fences or railings, lampposts and other miscellaneous equipment.

Since the dead load acting on a member must be assumed before the member is designed, one should

design the members of a structure in such a sequence that to as great extent as practicable the weight of

each member being designed is a portion of the dead load carried by the next member to be designed.

2.2. Imposed loads (Live loads)

Live loads can vary both in their magnitude and location. They may be caused by the weights of objects

temporarily placed on a structure, moving vehicles or natural forces. It is sometimes convenient to classify

live loads as moving loads and movable loads. Movable loads are those that can be moved from one

position to another on a structure ,such as the contents of a storage buildings. Moving loads are those that

move under their own power such as railroad train or a series of trucks. They are usually applied rather

rapidly and therefore exert an impact effect on the structure.

The live load for highway bridges consists of the weight of the applied moving loads of vehicles and

pedestrians. The live load for railroad bridges consists of locomotives and cars that cross it. The live load

for each track is usually taken as the live load corresponding to two locomotives followed by a uniform load

that represents the weight of the cars. Live loads for buildings are usually considered as movable

distributed loads of uniform intensity. The intensity of the floor loads to be used depends on the purpose

for which the building is designed.

Impact loads

Unless a live load is applied gradually, the deformation of the structure to which the live load is applied is

greater than it would be if the live load were considered as a static load. Since the deformation is greater,

the stresses in the structure are higher. The increase in stress due to live load over and above the value

that this stress would have if the live load were applied gradually is known as impact stress. Impact

stresses are usually associated with moving live loads. For purposes of structural design, impact stresses

are usually obtained by multiplying the live load stresses by a fraction called the impact fraction, which is

specified rather empirically.


Wind loads

Wind loads are particularly important in the design of large structures, such as tall buildings, radio towers

and long span bridges, for structures such as mill buildings and hangars that have large open interior and

walls in which large opening may occur. The effect of wind on a structure depends upon the density and

velocity of the air, the angle of incidence of the wind, the shape and stiffness of the structure and the

roughness of ground surface. Wind action fluctuate with time and act directly as pressures on the external

surfaces of enclosed structure because of porosity of the external surface, also act indirectly on the

internal surfaces. They may also get directly on the internal surface of open structures. Pressures act on

areas of the surface resulting in forces normal to the surface of the structure or individual cladding

components .Additionally when large areas of structure are swept by the wind, friction forces acting

tangentially to the surface may be significant. The wind pressure acting on the external surface of the

structure We shall be obtained as We = q ref Ce(Ze)Cpe and on the internal surface W i = qref Ce(Ze)Cpi where

qref = ρ Vref2/2 where ρ is the density of the air, Vref is the reference wind velocity.

Vref = CdirCtempCalt Vref,o. Vref,o is the basic value of wind velocity taken as 22 m/s. Cdir is the direction factor

taken as 1. Ctemp is seasonal factor taken as 1 and Calt is altitude factor taken as 1. Vref is defined as the 10

minute mean wind velocity at 10m above ground of terrain category II having an annual probability of

exceedence of 0.02. Ce(Ze) is the exposure coefficient accounting the effect of terrain roughness(whether

the structure is located near sea, lakes, clear land, farmlands or urban city) and topography(whether hills,

escarpment etc).Cpe is external pressure coefficient accounting the variation of wind velocity along the

height of the structure. The net pressure on a wall, roof or element is the difference b/n the pressure on

opposite surfaces taking due account of their signs. Pressure directed towards the surface is taken as

positive and pressure directed away from the surface is called suction and is negative. Examples are

shown below.


Earthquake loads

Important structures located in regions subjected to severe earthquake are often designed to resist

earthquake effects. During an earthquake ,structural damage may result from the fact that the foundation

of the structure undergoes accelerations. Such accelerations are largely horizontal and vertical

components are usually neglected. In active earthquake zones, the maximum rate of horizontal

acceleration of the foundation may reach having magnitude b/n 0.5 and 1 times gravity(9.81m/s2).The

seismic base shear force, Fb acting at the base of the structure causing movement for each main

direction(two orthogonal axis)is determined from

Fb = Sd(T1)W

where Sd(T1) is the ordinate of the design spectrum at period T1. T1 is fundamental period of vibration of

the structure for translational motion in the direction considered. T1 = C1 H3/4

where H is the height of the

building above the base in meters. C1 is coefficient accounting the frame type whether steel or reinforced

concrete frame. W is the seismic dead load.

Sd(T1) = αβγ

α is the ratio of the design bedrock acceleration to the acceleration of the gravity, g and is given as

α=αoI

where I is the importance factor which depend on the size of the building, on its value and importance for

the public safety and possibility of human losses in case of collapse. αo is the bedrock acceleration ratio of

the site.

The parameter β is the design response factor for the site and is given by

β=1.2S/T2/3

.

The factor S is the site coefficient for the soil characteristic on which the structure is founded. T is the

period considered.

The behavior factor γ account the energy dissipation capacity of the structure when the structure is under

earthquake load.

γ=γo kD kR kW ≤ 0.70,

γo is basic value of the behavior factor dependent on the structural type.

kD is factor reflecting the ductility class, kR -factor reflecting the structural regularity in elevation, kW -factor

reflecting the prevailing failure mode of structural system with walls.

The base shear force shall be distributed over the height of the structure as Fb = Ft +∑Fi The concentrated

force Ft at the top which is in addition to Fn shall be determined from Ft = 0.07T1Fb


The remaining portion of the base shear shall be distributed over the height of structure including level n

according to the following formula,

∑=

−

=n

i

ii

iitb

i

hW

hWFFF

1

)(

Hydrostatic and soil pressures

When structures are used to retain water, soil, or granular material, the pressure developed by these

loading is important criterion for their design. Examples of such types of structures include tanks, dams,

ships, bulkhead and retaining wall. The law of hydrostatics and soil mechanics are applied to define the

intensity of the loading on the structure.

Non-directional loads include thermal loads, shrinkage, fabrication error and support settlements

Thermal load

Changes in temperature cause strains in the members of a structure and hence produce deformations in

the structure as a whole. If the changes in shape due to temperature encounter restraint, as is often the

case in a statically indeterminate structure, stresses will be set up within the structure. The forces set up in

a structure as a result of temperature changes are often called thermal forces. In addition to considering

the forces set up by changes in temperature, it is important to take into consideration the expansion and

contraction of a structure, particularly in connection with support details.

Shrinkage

Among the widely used materials, concrete is most susceptible to shrinkage. A length L of freshly poured

concrete shortens an amount sL as it sets. The coefficient s is called shrinkage ratio. Most specifications

prescribe a constant value for s. For concrete, on the average, s =0.0003. During shrinkage ,if a structural

resistance occurs, internal stresses will develop. In fact this is the case in statically indeterminate

structures.

Fabrication errors

Owing to the lack of appropriate quality control, the elements of a structure may have different dimensions

and shapes than their design dimensions and shapes. The difference is called the actual fabrication error.

In indeterminate structure these fabrication errors cause stresses.

Support settlements

If a structure is supported in a statically indeterminate manner and the supports settle unevenly, then

stresses will develop. Since the internal stresses will be large when the differential settlements are large, a

designer need to be refrained from using statically indeterminate support states in sites where the

expected differential settlements are large.


2.3. Factor of safety

Whenever a structure is designed, it is important to give consideration to both material and load

uncertainties. To account these uncertainties and the structure to be safely carry loads, factor of safety is

included. According to EBCS-1, the design value of material property is generally defined as

Xd = Xk/γm

where Xk is the characteristic strength value of material. The characteristic strength is the material strength

below which, not more than a prescribed percentage of the test result fall. For example, EBCS-2 specifies

the characteristic compressive strength of concrete as the strength below which 5% of all possible strength

measurement is expected to fall. Where γm is the partial safety factor for the material for product property

which covers a) unfavorable deviations from the characteristics values, b) inaccuracies in the conversion

factors c) uncertainties in the geometric properties and resistance model.

The load considered for design is obtained from characteristics load multiplied with safety factor, γF

Fd = γFFK .

The characteristic load FK and is defined as the value of load which has an accepted probability of not

being exceeded during the life span of structures. γF is the partial safety factor for the action considered

taking account of the possibility of unfavorable deviations of the action, the possibility of inaccurate

modeling of the action and uncertainties in the assessment of effects of action.

2.4. Load combinations

The many types of loads discussed previously can occur simultaneously on a structure, but it is very

unlikely that the maximum of all these loads occur at the same time. For example, the load combination for

assuring against failure by strength criteria for structural design of building is given in EBCS-1 as follows

combination one :Dead load and one live load

Fd =1.3(dead load) +1.6(live load)

Combination two: Dead load and two or more live loads

Fd =1.3(dead load) +1.35(∑(live load))

Combination three: Dead load, dominant of live loads and accidental (earthquake)load

Fd = dead load + dominant live load + earthquake load

In all these cases, the combination of loads is thought to provide a maximum yet realistic loading on the

structure.

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