EXCAVATION CALCULATION BASIC INFORMATION AND TUTORIALS

Excavation is measured by the cubic yard for the quantity takeoff (27 cf # 1 cy). Before excavation, when the soil is in an undisturbed condition, it weighs about 100 pounds per cf; rock weighs about 150 pounds per cf.

The site plan is the key drawing for determining earthwork requirements and is typically scaled in feet and decimals of a foot. There is usually no reason to change to units of feet and inches; however, at times they must be changed to decimals. Remember that when estimating quantities, the computations need not be worked out to an exact answer.

Swell and Compaction.

Material in its natural state is referred to as bank materials and is measured in bank cubic yards (bcy). When bank materials are excavated, the earth and rocks are disturbed and begin to swell.

This expansion causes the soil to assume a larger volume; this expansion represents the amount of swell and is generally expressed as a percentage gained above the original volume.

Uncompacted excavated materials are referred to as loose materials and are measured in loose cubic yards (lcy).When loose materials are placed and compacted (as fill) on a project, it will be compressed into a smaller volume than when it was loose, and with the exception of solid rock it will occupy less volume than in its bank condition.

This reduction in volume is referred to as shrinkage. Shrinkage is expressed as a percentage of the undisturbed original or bank volume.

Materials that have been placed and compacted are referred to as compacted materials and are measured in compacted cubic yards (ccy). Bank, loose, and compacted cubic yards are used to designate which volume we are talking about.

Figure 9.1 is a table of common swell and shrinkage factors for various types of soils. When possible tests should be performed to determine the actual swell and shrinkage for the material.

FIGURE 9.1. Swell and Shrinkage Factors. (Solid rock when compacted is less dense than its bank condition.)

SEISMIC LOAD ON ROOFS DESIGN AND CALCULATION BASIC AND TUTORIALS

SEISMIC LOAD ON ROOFS DESIGN AND CALCULATION BASIC INFORMATION
How To Make Seismic Load On Roofs Design and Calculation?


Seismic Loads Calculations
The engineering approach to seismic design differs from that for other load types. For live, wind or snow loads, the intent of a structural design is to preclude structural damage. However, to achieve an economical seismic design, codes and standards permit local yielding of a structure during a major earthquake.

Local yielding absorbs energy but results in permanent deformations of structures. Thus seismic design incorporates not only application of anticipated seismic forces but also use of structural details that ensure adequate ductility to absorb the seismic forces without compromising the stability of structures.

Provisions for this are included in the AISC specifications for structural steel for buildings. The forces transmitted by an earthquake to a structure result from vibratory excitation of the ground. The vibration has both vertical and horizontal components.

However, it is customary for building design to neglect the vertical component because most structures have reserve strength in the vertical direction due to gravity-load design requirements. Seismic requirements in building codes and standards attempt to translate the complicated dynamic phenomenon of earthquake force into a simplified equivalent static force to be applied to a structure for design purposes.

For example, ASCE 7-95 stipulates that the total lateral force, or base shear, V (kips) acting in the direction of each of the principal axes of the main structural system should be computed from
V = CsW(9.139)

where Cs seismic response coefficient
W total dead load and applicable portions of other loads

The seismic coefficient, Cs, is determined by the following equation:
Cs = 1.2Cv /RT^2/3(9.140)

where Cv seismic coefficient for acceleration dependent (short period) structures
R response modification factor
T fundamental period, s

Alternatively, Cs need not be greater than
Cs = 2.5Ca/R(9.141)

where Ca seismic coefficient for velocity dependent (intermediate and long period) structures.

A rigorous evaluation of the fundamental elastic period, T, requires consideration of the intensity of loading and the response of the structure to the loading. To expedite design computations, T may be determined by the following:
Ta = CThn^3/4(9.142)

where CT 0.035 for steel frames
CT 0.030 for reinforced concrete frames
CT 0.030 steel eccentrically braced frames
CT 0.020 all other buildings
hn height above the basic to the highest level of the building, ft

For vertical distribution of seismic forces, the lateral force, V, should be distributed over the height of the structure as concentrated loads at each floor level or story. The lateral seismic force, Fx, at any floor level is determined by the following equation:
Fx = CuxV(9.143)

where the vertical distribution factor is given by

(9.144)

where wx and wi height from the base to level x or i
k 1 for building having period of 0.5 s or less 2 for building having period of 2.5 s or more  use linear interpolation for building periods between 0.5 and 2.5 s


For horizontal shear distribution, the seismic design story shear in any story, Vx, is determined by the following:

 (9.145)

where Fi the portion of the seismic base shear induced at level i. The seismic design story shear is to be distributed to the various elements of the force resisting system in a story based on the relative lateral stiffness of the vertical resisting elements and the diaphragm. Provision also should be made in design of structural framing for horizontal torsion, overturning effects, and the building drift.

WIND LOADS ON ROOFS DESIGN AND CALCULATIONS BASIC AND TUTORIALS

WIND LOADS ON ROOFS DESIGN AND CALCULATIONS BASIC INFORMATION
Wind Load Calculations On Roofs For Design


Wind Loads Calculation
Wind loads are randomly applied dynamic loads. The intensity of the wind pressure on the surface of a structure depends on wind velocity, air density, orientation of the structure, area of contact surface, and shape of the structure.

Because of the complexity involved in defining both the dynamic wind load and the behavior of an indeterminate steel structure when subjected to wind loads, the design criteria adopted by building codes and standards have been based on the application of an equivalent static wind pressure.

This equivalent static design wind pressure p (psf) is defined in a general sense by
p = qGCp (9.136)

where q velocity pressure, psf
G gust response factor to account for fluctuations in wind speed
Cp pressure coefficient or shape factor that reflects the influence of the wind on the various parts of a structure

Velocity pressure is computed from
qz = 0.00256 KzKztKdV^2I (9.137)


where Kz velocity exposure coefficient evaluated at height z
Kzt topographic factor
Kd wind directionality factor
I importance factor
V basic wind speed corresponding to a 3-s gust speed at 33 ft above
the ground in exposure C


Velocity pressures due to wind to be used in building design vary with type of terrain, distance above ground level, importance of building, likelihood of hurricanes, and basic wind speed recorded near the building site.

The wind pressures are assumed to act horizontally on the building area projected on a vertical plane normal to the wind direction.

ASCE 7 permits the use of either Method I or Method II to define the design wind loads. Method I is a simplified procedure and may be used for enclosed or partially enclosed buildings.

ASCE 7 Method II is a rigorous computation procedure that accounts for the external, and internal pressure variation as well as gust effects. The following is the general equation for computing the design wind pressure, p:
p = qGCp qi(GCpt) (9.138)

where q and qi velocity pressure as given by ASCE 7
G gust effect factor as given by ASCE 7
Cp external pressure coefficient as given by ASCE 7
GCpt internal pressure coefficient as given by ASCE 7

Codes and standards may present the gust factors and pressure coefficients in different formats. Coefficients from different codes and standards should not be mixed.

SNOW LOADS ON ROOFS DESIGN AND CALCULATIONS BASIC AND TUTORIALS

SNOW LOADS ON ROOFS DESIGN AND CALCULATIONS BASIC INFORMATION
What Are Snow Loads On Roofs Design And Calculations


Snow Loads Calculation
Determination of designing snow loads for roofs is often based on the maximum ground snow load in 50-year mean recurrence period (2% probability of being exceeded in any year).

This load or data for computing it from an extreme-value statistical analysis of weather records of snow on the ground may be obtained from the local building code or the National Weather Service.

Photo courtesy of Ask The Builder

Some building codes and ASCE 7-95 specify an equation that takes into account the consequences of a structural failure in view of the end use of the building to be constructed and the wind exposure of the roof:

pf = 0.7CeCtIpg (9.134)

where Ce wind exposure factor (range 0.8 to 1.3)
Ct thermal effects factor (range 1.0 to 1.2)
I importance factor for end use (range 0.8 to 1.2)
pf roof snow load, lb per ft2
pg ground snow load for 50-year recurrence period, lb per ft2

The “Low-Rise Building systems Manual,” Metal Building Manufacturers Association, Cleveland, Ohio, based on a modified form of ASCE 7, recommends that the design of roof snow load be determined from

pf = IsCpg(9.135)
where Is is an importance factor and C reflects the roof type.

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SHEAR AND BENDING MOMENT DIAGRAMS BASICS AND TUTORIALS

SHEAR AND BENDING MOMENT DIAGRAMS BASIC INFORMATION
A Tutorials on Shear and Bending Moment Diagram? How To Make Shear and Bending Moment Diagram


In order to plot the shear force and bending moment diagrams it is necessary to adopt a sign convention for these responses. A shear force is considered to be positive if it produces a clockwise moment about a point in the free body on which it acts.

A negative shear force produces a counterclockwise moment about the point. The bending moment is taken as positive if it causes compression in the upper fibers of the beam and tension in the lower fiber. In other words, sagging moment is positive and hogging moment is negative.

The construction of these diagrams is explained with an example given in Figure 2.4.

The section at E of the beam is in equilibrium under the action of applied loads and internal forces acting at E as shown in Figure 2.5. There must be an internal vertical force and internal bending moment to maintain equilibrium at Section E.

The vertical force or the moment can be obtained as the algebraic sum of all forces or the algebraic sum of the moment of all forces that lie on either side of Section E.

The shear on a cross-section an infinitesimal distance to the right of pointAisC55 k and, therefore, the shear diagram rises abruptly from 0 to C55 at this point. In the portion AC, since there is no additional load, the shear remainsC55 on any cross-section throughout this interval, and the diagram is a horizontal as shown in Figure 2.4. 

An infinitesimal distance to the left of C the shear is C55, but an infinitesimal distance to the right of this point the 30 k load has caused the shear to be reduced to C25. 

Therefore, at point C there is an abrupt change in the shear force from C55 to C25. In the same manner, the shear force diagram for the portion CD of the beam remains a rectangle. In the portion DE, the shear on any cross-section a distance x from point D is 

               S = 55 − 30 − 4x D 25 − 4x

which indicates that the shear diagram in this portion is a straight line decreasing from an ordinate of C25 at D to C1 at E. 

The remainder of the shear force diagram can easily be verified in the same way. It should be noted that, in effect, a concentrated load is assumed to be applied at a point and, hence, at such a point the ordinate to the shear diagram changes abruptly by an amount equal to the load.

In the portion AC, the bending moment at a cross-section a distance x from point A isM D 55x. Therefore, the bending moment diagram starts at 0 at A and increases along a straight line to an ordinate of C165 k-ft at point C. 

In the portion CD, the bending moment at any point a distance x from C is M D 55.x C 3/ − 30x. Hence, the bending moment diagram in this portion is a straight line increasing from 165 at C to 265 at D. In the portion DE, the bending moment at any point a distance x from D is M D 55.x C 7/ − 30.X C 4/ − 4x2=2. 

Hence, the bending moment diagram in this portion is a curve with an ordinate of 265 at D and 343 at E. In an analogous manner, the remainder of the bending moment diagram can be easily constructed.

Bending moment and shear force diagrams for beamswith simple boundary conditions and subject to some simple loading are given in Figure 2.6.

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