# Example 7:flexural stress for triangle shape beam using transform area method

Knowing the dry density of soil or pavement is important to evaluate the degree of compaction achieved during the construction process. A field density test is a common test used to determine the field density of the soil or pavement. The principle of field density test is the replacement of soil excavated materials by the sand, the sand density is known so we can calculate the volume of the sand required to fill the hole. By knowing the volume of the hole excavated in soil and the weight of soil, we can calculate the in-situ density. The in-situ density equals the weight of excavated materials divided by the volume of excavated material. Apparatus  Sand pouring cylinder equipment

Small sand pouring cylinder equipment: this suitable for fine and medium-grained soil. It consists of a cylinder having a diameter of 100 mm and a length of 380 mm with an inverted funnel at one end and a shutter to open and close for the entry of sand. Also, there will be a metal tray for the excavation of s…

Design a one-way slab for the inside of a building using the span, loads, and other data given in Figure 1. Normal-weight aggregate concrete is specified with a density of 145 pcf. (assuming cover 3/4 in) Figure 1

The minimum thickness for one-way slab simply supported=L/20 using table 1(ACI 9.5.2.1) h=10/20=0.5=6in

Table 1

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now we will calculate d=(6-3/4(cover)-1/4(estimated as half diameter of reinforcement) d=5 in
now we will calculate dead load concrete density=145pcf, Usually 5 pcf is added to account for the weight of reinforcement, so 150 pcf is used in calculating the weight of a normal-weight concrete member. dd=(6in*ft/12)*1*150/=75 lb/ft LL=200*(1)=200lb/ft Wu=1.2*75+1.6*200=410 lb/ft
maximum moment for simply supported span =(Wu*L^2)/8 =(410*10^2)/8=8/=5,125lb-ft=61,500lb-in
now we can calculate ρ
ρ=(0.85*fc’/fy)*(1-√(1-(2*Rn/0.85*fc’))

Rn=Mu/(ϕ*b*d^2) Rn=(61500)/(0.9*12*(5^2))=227.7

ρ=… Da structure can be called determinate if the equilibrium equation provides enough and sufficient condition for equilibrium. if all forces for a structure can be determined using equilibrium equations only, this structure is determinate, but if the unknown forces are more and cant be determined using equilibrium equations then this structure is indeterminate.in general we can determine if a structure is statically determinate or indeterminate by drawing free body diagram for a structure or part of it and comparing a number of unknown forces and moment component with number of available equation of equilibrium. for coplanar structures, we have  three equilibrium equations, if n is the total number of parts and r is the number of unknown forces and moment component then:

r=3*n determinate r>3*n indeterminate

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statically indeterminate structure cant be solved using equilibrium equations, so…

Pile cap used to transfer the loads from superstructure to the piling. The pile cap is thick concrete mat rests on piles. It is part of the foundation and used to distribute the loads over the piles. Piles used when the soil bearing is not enough to carry loads of the structure.

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Pile cap construction procedure Excavation around piles: After 7 days of the casting of the pile the concrete will gain approximately, 70% of it is compressive strength. The soil around piles will be removed to the required levels and dimension that allows construction of the pile cap. A step shall be made if the excavation is more than 1.5 m to prevent soil collapse. Pile head cutting: Concrete will be removed up to cut off level. If concrete under the cut off level is unsound. It shall be removed, and the pile will be repaired. Pile must be free from cracks and unsound concrete.

Blinding concrete: after completion o…

In a truss system, some members are not carrying any force. This called zero-force member. This member may added to increase truss stability. Identifying these members will simplify the process of analyzing truss. the determination of zero force member can be done by inspecting of truss joints, and there are two casesif we check the joint c for truss shown in figure 1, this joint has no external load, and two members are connected to this joint at a right angle. if we sum force in y-direction Σfy=0, we get FCD=0, similarly in x-direction FCB=0. For joint A, no external load applied to this joint. If we sum forces in y-direction Σfy=0, we get FAB=0. Similarly, in x-direction FAE=0. Figure 1

A quick look at this truss. We can notice joint c and joint d with no external load. Inspecting joint C will be a bit difficult because 4 members are connected to joint c. Starting with joint D. member DF is perpendicular to member DE and CD. if we sum the forces in the y-direction. As showing in fig…

Flaky and elongated aggregates can adversely affect concrete. Flaky and elongated aggregates are difficult to compact. Therefore using flaky and elongated aggregates will reduce concrete workability, which required more amount of water to produce a workable mix. Increasing water content will reduce concrete strength and durability. Moreover, these aggregates are not robust, which leads to lowering concrete strength. Figure 1

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The Flakiness Index of aggregates is the percentage by weight of particles whose least dimension (thickness) is less than three- fifths (0.6times) of their mean dimension. This test does not apply to sizes smaller than 6.3mm.

The Elongation index of an aggregate is the percentage by weight of particles whose greatest dimension (length) is greater than nine-fifths (1.8times) their mean dimension. Flakiness and elongation tests are not applicable to sizes smaller than 6.3…

Let consider a slab supported by beams and columns, to begin structural analysis for each member, we need to know the amount of load transferred to this member, the amount of load transferred to any member can be determined using tributary area(loading) concept. the geometry of a structure will determine the shape of the tributary area. figure 1

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In a one-way system, slab delivers the load to supports by one-way action. the dimension of slab shall satisfy the following equation to act as one-way slab L2/L1>2. let consider floor system in figure 3, L2/L1 for beam AB L2/L1=15/5=3, therefore slab will transfer the loads to beam in one-way action, tributary area for beam AB, E-f will be as shown in figure 3, loads of 100*2.5=250Lb/ft(linearly distributed over the whole length of the beam, for beam CD, the load will be 100*5=500Lb/ft, beam CD will share loads from both sides because it is lo…

A prime coat is the application of low viscosity bituminous materials to the absorptive surface to penetrate, bond, and stabilize the existing surface before laying the asphalt mix. Usually, the prime coat is applied above the aggregate base coarse or granular bases that will receive the asphalt layer. While the tack coat is applied between two layers of asphalt. Tack coat is a very light application of bituminous materials to ensure proper bonding between two binder layers. Figure 1

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bridge construction:How to become a bridge engineer the benefits of using prime coat are as follow: · Prime coat will penetrate and fill the voids of the granular base course. Also, it will coat and bond the mineral particles in the base course to produce a tough and tight surface to receive the binder layer.

· Prime coat will waterproof the granular base course, which provides protection from the wet weather. The prime coat will prevent the base …

Punching shear is a type of failure that occurs on slabs due to high localized loads. In flat slab, this occurs at the columns supports, as shown in figure no:1. The dead and live load of the slab will generate a high shear force around the column’s support. If the columns are not well reinforced or the cross-section of columns is not big enough, the punching shear will occur. We can see in figure no:2 that the columns support failed due to punching shear, the columns in this figure seem to punch and penetrate the slabs. Figure 1 Figure 2 The designer should consider punching shear during the design stage. The punching shear design will involve the following steps: ·Checking if the concrete is strong enough to resist punching shear ·If no, we need to add sufficient reinforcement to resist punching shear ·Or we can increase the concrete thickness around the columns and this can be done by introducing drop panels, increase the slab thickness or increasing the column cross-section.

For t…

Various methods used to construct cast in-situ piles. In general, the concept is the same; however, there is a minor difference between these methods. Bored piles diameter ranges from 600 mm to 3000 mm, and the bored pile depth can reach up to 70 m. This provides the designer with great freedom in customizing foundation design according to site condition and optimizing the cost to produce the economical design.

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cast in-situ piles method of construction Casing punching

Casing depth can vary depends on site condition and soil properties. Length of the casing should be increased in case of loose oil. Using bentonite can help in preventing soil collapse. The casing length will be reduced. If bentonite used.  The primary function of the casing is to prevent soil collapse in the event of loose soil and absent of soil supporting liquid. Also, it will enable the land surveyor to verify pile location a…