Video from my YouTube channel

Subscribe to My You tube channel

Example 2: design of rectangular beam

By -
design rectangular sections for the beams, loads, and ρ values shown. Beam weights are not included
in the loads shown. Show sketches of cross sections, including bar sizes, arrangement, and spacing. Assume concrete weighs 150 lb/ft3 , fy= 60,000 psi, and fc'= 4000 psi, unless given otherwise.

Figure 1









first, we will calculate the ultimate load, we have point live load and distributed dead load, therefore we will take each load separately

ultimate live load=1.6*PL=1.6*20=32k

assuming the weight of beam=0.40k/ft
dead load=2+0.4=2.4 k/ft
ultimate dead load=1.2*2.4=2.88k/ft

the ultimate moment will be at the mid of beam= 50.56*12-2.88*12*6=399.36k-ft


Mu=Ф*Mn=Ф*Asfy(d-a/2)    

Mu/(b*d^2)=Ф*ρ*fy(1-fy*ρ/1.7*fc')    

ρ=0.18*4,000/60,000=0.012

bd^2=Mu/(Ф*ρ*fy(1-fy*ρ/1.7*fc')   assuming Ф=0.90

Mu=399.36K-ft=4,792,320lb-in

bd^2=4,792,320/(0.9*.012*60,000*(1-60,000*0.012/1.7*4000))=8,271.34

bd=    12x27
          14x24

using 14*28 as beam dimension (bxh)

checking beam weight=14*28*150/144=0.40k/ft    ok


As=ρ*b*d=0.012*14*24=4.032in2

 using 3#11=3*1.56=4.68 in2


checking for Ф=0.9 or no

(εt+0.003)/(d)=0.003/c

C=a/β1

β1=0.85 for fc'=4000 psi or less

 a=Asfy/(0.85*fc'*b)

a=4.68*60,000/(0.85*4000*14)=5.9in

C=a/β1=5.9/0.85=6.94in

εt=0.003*(24.3)/C-0.003=0.0075>0.005 so section is tension control Ф=0.9  is ok

checking for ρmin

As,min=(3√fc'/fy)*bw*d and not less than 200bw*d/fy

As,min=3*√4000*14*24.3/60,000  and not less than 200*24.3*14/60,000

As,min=1.075 in2 and not less than 1.134in2 ok, our As is larger than the minimum 

checking Ф*Mn>Mu

Ф*Mn=0.9*4.68*60,000(d-a/2)


Ф*Mn=0.9*4.68*60,000(24-5.9/2)=5,319,756> Mu







Comments

Post a Comment

Videos from My Youtube channel

Popular posts from this blog

why do we stagger reinforcement overlapping?

By -
Image
First, we should know that steel rebar comes in standard length such as 12m. using very long reinforcement is impractical because it will result in difficulties in handling reinforcement by steel fabricators. Also, longer rebar is heavier and difficult to lift and move. So for a long structure such as a slab, we require a reinforcement length that is more than the standard reinforcement. We can't use a single piece of rebar for a specific length for such a structure, so we use two or more steel rebars to cover the entire length of the structure. Figure no:1 The zone of overlapping between reinforcement will be considered as a weak zone. Therefore, it is a good practice to stagger the reinforcement overlapping. Staggering is done by overlapping the reinforcement at a different location. Staggering reinforcement overlapping will reduce the number of rebars overlapped at the same point, which will be beneficial in two ways. Firstly, it will reduce the discontinuity of rebar at the s...
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

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

Rebar Splicing and Overlapping — ACI 318-19 Requirements Explained

By -
Image
Reinforcement splicing or overlapping is a fundamental requirement in reinforced concrete structures. Because reinforcement bars (rebars) are manufactured in limited standard lengths—typically 12 m —it becomes necessary to splice or overlap them to achieve the required continuity in structural members. The main purpose of a splice is to ensure smooth stress transfer between adjacent bars through the surrounding concrete. The overlap length, commonly known as the splice length , must be long enough to safely transfer the tensile stresses from steel to concrete without causing bond failure. It is recommended to avoid splicing in high-stress zones such as areas of maximum moment, and to stagger the splices to prevent congestion and reduce stress concentration. The ACI 318-19 providing the following recommendatin and requirement for the lap splicing: 1. Splice Limitation by Bar Size Lap splicing is not permitted for reinforcement bars larger than 36 mm in diameter. 2. Non-Contact L...
Read more

Prestressing stands debonding

By -
Image
  Prestressing bridge concrete beams contributes to resisting the tensile stresses caused by the traffic loads and the beam's weight. Stressing concrete has various benefits, such as increasing concrete members' capacity, reducing the concrete member section, and increasing the span lengths for structures such as bridges and buildings. However,  The stressing of bridge beam ends can result in unwanted cracks. Therefore AASHTO calling for debonding a specific portion of strands at the beam end to minimize the stresses and reduce cracks. Figure 1 Debonding is achieved by wrapping the strands at the end of the beam with plastic. Wrapping the strand with plastic wrapping will prevent the strands from bonding with concrete, thus avoid transferring unwanted stress to the beam end. As a result, the unwanted cracks will be prevented by reducing the stress levels at the end of the beam.  
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

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

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

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

Prestressing strand manufacturing

By -
Image
  Prestressing strands is high tensile strength steel. The tensile strength of prestressing strands can reach up to 1860 Mpa. the process of manufacturing prestressing steel differs significantly from the conventional reinforcement.  Figure 1 The process of manufacturing strands will begin by de-scaling the raw material (wire rod). The purpose of de-scaling is to remove the iron oxides (mill scale) from the surface of the wire rod. after removing the mill scale, the wire rod's surface is coated with a textured coating to enhance the adherence of lubricants to the raw material surface. The most commonly used coating is zinc phosphate.  Figure 2 The wire rod then passed through a series of dies. The process of reducing the wire rod diameter is known as cold-drawing. In this process, the wire rod is drawn through a die with the required diameter. To prevent the wearing of dies, the wire rod will be drawn through a lubricant box. the lubricant will coat the wire with a thin l...
Read more