Video from my YouTube channel

Subscribe to My You tube channel

Example 5: allowable uniform load can beam support using transformed area method

By -
Using transformed area, what allowable uniform load can this beam support in addition to its own
weight for a 28-ft simple span? Concrete weight = 150 lb/ft3 ,fs= 24,000 psi, and fc= 1800 psi.






Figure 1             


Transform area=As*n
As=1.27*5=6.35in4
Transform area=6.35*8=50.8in2

Location of neutral axis by equalling moment of area around neutral axis as shown in figure 2(assuming neutral axis below the void)

X(20)(X/2)-8*8*(x/2-4)=50.8*(29-X)
10X^2-32X+256=1473.2-50.8X
10X^2+18.8X-1217.2=0
X=10.3, assumpitation is not valid

Assuming X in void area as shown in figure 3


X(20)(X/2)-8*(X-4)*(x-4)/2=50.8*(29-X)
10X^2-4(X^2-4X-4X+16)-1473.2+50.8X=0
10X^2-4X^2+32X-64-1473.2+50.8X=0
6X^2+82.8X-1409.2=0
X=9.91in

now we will calculate moment of inertia using parallel axis theorem 

I=20*(9.91^3)/12+20*9.91*4.955^2-((8*5.91^3)/12+5.91*8*2.955^2)+50.8*19.09^2
I=24450.76in4=1.18ft4




Figure 2

Figure 3

the moment for extreme compression fiber for y=9.91in
M=fcI/y
M=1800*24450.76/9.91
=4441106.76lb-in
=370.09k-ft
from the moment we can calculate the load 
M=WL^2/8
W=M*8/L^2
W=370.09*8/(28^2)=3.776K

the moment at the center of reinforcing rebar for y=19.09in

fs=n*M*y/I
M=fs*I/(n*y)
M=24000*24450.76/(19.09*8)
=3842445.259lb-in
=320.20k-ft

M=WL^2/8
W=M*8/L^2
W=320.2*8/(28^2)=3.27K

we will select the lowest load from above W=3.27K(including beam own weight)
W without beam own weight=3.27-0.15*(32*20-8*8)/144=2.67k/ft









Comments

  1. struturalAugust 22, 2020 at 11:19 PM

    This comment has been removed by the author.

    ReplyDelete
  2. AnonymousAugust 25, 2020 at 9:27 AM

    you have error : x not equal x = 9.91 , your -64-1473.2 = -1537.2 , you can also easily calc moment of inertia as : bh^3/3+bh^/3+As*D^2 , Saudi Eng bypass from here. good luck mohammed.

    ReplyDelete

Post a Comment

Videos from My Youtube channel

Popular posts from this blog

Pile cap

By -
Image
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. Figure 1  construction management: concrete construction bridge construction:How to become a bridge engineer 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. Figure 2 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...
Read more

Bridge Diaphragm

By -
Image
The main function of diaphragms is to provide a stiffening effect to deck slab in case bridge webs are not situated directly on top of bearings. Therefore, diaphragms may not be necessary in case bridge bearings are placed directly under the webs because loads in bridge decks can be directly transferred to the bearings.On the other hand, diaphragms also help to improve the load-sharing characteristics of bridges. Diaphragms also contribute to the provision of torsional restraint to the bridge deck. Diaphragm will be used also to resist stresses that occurs during the post-tensioning process. Post-tensioning hardware are casted inside the diaphragm. Figure 1 construction management: concrete construction bridge construction:How to become a bridge engineer Types of diaphragm: Diaphragm at the span end: this type of diaphragms will be located between two bridge spans or at the bridge abutments. Expansion joints will be used to connect bridge spans. This ...
Read more

stress-strain diagram for aluminium alloy and rubber

By -
Image
figure no:1 showing the stress-strain diagram for aluminum alloy. we can notice from the stress-stress diagram that aluminum has a considerable ductility. despite the absence of explicit yield point as in structural steel . the initial portion of the stress-strain curve is linear with a recognizable proportional limit. the proportional limit for aluminum alloy ranges from 70 to 410 Mpa (10 to 60 Ksi). aluminum alloy undergoes large strain before failure. ultimate stress ranges from 140 to 550 Mpa (20 to 80 Ksi). construction management: concrete construction bridge construction:How to become a bridge engineer Figure-1 Yield stress for aluminum alloy can be determined by drawing offset line parrel to the linear portion of the stress-strain curve. the straight line offset by a standard strain such as 0.002. the intersection point with the stress-strain curve is the point of yield stress. figure no:2 illustrates the concept of offset method. yield stress acquire...
Read more

Repairing of concrete bulging

By -
Image
Improper designing and installation of formwork for a concrete member can result in concrete Bulging. During the placing and compacting of concrete, forms may deflect largely in the weak areas. The deflection of forms will cause concrete to expand at this location, and this known as concrete Bulging. Concrete Bulging will spoil the appearance of a concrete member. Therefore we should always ensure that the forms are appropriately installed, and it is sufficiently supported to resist the concrete during placing and compacting. Bulging should be repaired in case we couldn't avoid it. The solution of concrete Bulging, offset, or surface irregularities are surface grinding. However, excessive surface grinding can weaken the concrete.  Figure 1 If the bulging or surface irregularities are small, grinding of concrete surface will be sufficient to remove surface irregularities. If the Bulging of concrete is significant, then the concrete should be chipped, and the surface...
Read more

Fire resistive construction-firewalls

By -
Image
The fire-resistive construction method will involve the designing and construction of fire resisting elements such as firewalls, fire barriers, fire partitions, smoke barriers, and smoke partition. The purpose of these components is to restrict the spread of fires between building units. Firewalls should be continuous from the foundation to the building roof, and it should have sufficient stability to resist the collapsing if the construction on either side collapse. Firewalls used to separate a structure into multiple units, which reduce the severity and consequences of fires by limiting the fire in one area and prevent the spreading of the fires to other structures area. Fire barriers and partitions are interior walls used to sub-divide the portion of a building that concealed by firewalls into smaller areas. Fire barriers and walls will be supported by the adjacent structure. They will prevent the heat flows within the area concealed by firewalls, which gives the residents suf...
Read more

Chamfers for concrete structures

By -
Image
In general, the edges of concrete members are chamfered. Usually during the process of installing forms for a structural member such as pile cap, a chamfer a PVC chamfer as shown in figure no:1 installed at the edges of the structural members. These chamfers will form smooth slanted edges, as shown in figure no:2. The size of chamfers can be 20x20mm or more as shown on the contract drawing. The PVC chamfer fixed to forms by nails. We should ensure that the PVC chamfer fixed in their correct locations, and we should ensure that the PVC chamfer is straight and not moving up or down. Checking the alignment and location of PVC chamfer is important, so the chamfered concrete edge will have a good appearance after the form’s removal.  Figure 1 Figure 2 Chamfering the concrete edges done for many reasons such as aesthetics, some suggesting that the chamfering of concrete edges done for safety to reduce the damage of objects due to impact with sharp concrete edges. Actually, ...
Read more

Equivalent Single Axle Load (ESAL) in Pavement Design

By -
Image
In pavement engineering, determining the Equivalent Single Axle Load (ESAL) is a crucial step in designing a durable and efficient roadway. ESAL simplifies the complexity of mixed traffic loading by converting it into a single representative value, allowing engineers to assess the cumulative impact of various vehicle types on pavement performance. The Concept of ESAL Roadways are subjected to traffic from a wide range of vehicles, each with different axle configurations and weights. Since these vehicles exert varying degrees of stress on the pavement, ESAL provides a standardized measure to represent their combined effect. The core idea behind ESAL is to express the cumulative traffic load on a road pavement as an equivalent number of passes of a standard axle load. This standard axle load is typically set at 80 kN . For example, if a road is subjected to an ESAL value of 10,000,000 , it means the pavement experiences the same level of stress as 10 million passes of a single standard...
Read more

Binding wire for steel reinforcement

By -
Image
  Binding wires are used to tie steel bars together. These wires are playing a significant role in maintaining the reinforcement stability and rigidity. Wires are used to tie the steel bars at intersections points. By tying the steel bars together, we ensure that the steel bars will not move from their locations during construction or during the time of concreting. In slabs, binding wires are used to tie longitudinal and transverse bars together. In columns, it is used to tie vertical bars with stirrups.   Figure 1 There are various types of binding wires such as  Black annealed baling wire, Stainless Steel Binding Wire, and PVC coated binding wires.  Black annealed baling wire used to tie black steel. The popular size for black wire ranges from 16 to 22 gauges. Stainless steel binding wires are used to bind stainless steel reinforcement. Stainless steel reinforcement is used in a harsh environment where the black steel gets rusted quickly. Therefore, stainless ...
Read more

Non-Working Pile Testing and Static Compression Load Test

By -
Image
Purpose of Non-Working Piles Non-working piles are constructed at the beginning of the project to evaluate soil bearing capacity and determine the maximum settlement. These piles are loaded up to twice the working load. Based on the test results, the pile length may be adjusted. If the measured settlement exceeds the allowable limit, the pile length will be increased accordingly. construction management: concrete construction bridge construction:How to become a bridge engineer Static Compression Load Test The static compression load test provides insight into how the pile responds to loading. Settlement is measured at different load increments to determine the appropriate pile design length. The maximum applied load is typically twice the working load (2 × working load) or as specified by local standards. The following steps outline the testing procedure: A. Steel Cage Preparation The steel reinforcement cage is prepared in accordance with the approved shop drawings. ...
Read more