CALCULATION FOR FIXED END MOMENTS FOR A SINGLE SPAN FIXED BEAM SUBJECTED WITH A POINT LOAD AT IT’S CENTRE

Mohammad Sohel Akhtar, Structural Engineer, New Delhi, India

“Feel the structure”

Here,at the end of this article, you will find an attachment having calculations to find out the fixed end moments for a single span fixed beam which is subjected with a point load at it’s centre.

Principle of superposition and compatibility equation has been used to find the fixed end moments. You will be astonished ,how tricky it has been to convert an indeterminate beam to few determinate beams. All converted determinate beams when added represents the same indeterminate beam and calculating deflection individually for each converted determinate beams and adding them all at specified location so that equation of compatibility can be formed will help us to find out the internal forces like moments & shear .

To understand the entire concept, please go through the attached calculation sheet and i am 100% sure, you will find it very different from any text books. Also, you may not have the same procedure in the text books as most of the text book does not go in so much deep to find out fixed end moments in simpler manner.I have explained step by step the entire concept.

In the calculation sheet, i have not explained how to determine BMD & M/EI diagram as it is not our subject of analysis. Our focus of analysis is to determine fixed end moments. Anyway, please visit my previous blogs in the Category of deflection calculation in which i gone in details for the formation of BMD & M/EI diagram.

People are scared on analyzing complex indeterminate structure because they think it a complex. If using good judgement,you are able to convert any indeterminate beam to simpler determinate beams, then i ensure you that your half of work is done and you will be solving only simple equations.

As a structural engineer, we should not ignore analysis of cantilever beams subjected with different kind of loading. You will notice, if you are able to solve for cantilever beams then you will be able to a frame structure. Firstly, building is nothing but a vertical cantilever and during analysis of any frame, we should have a great judgement and skill to convert frames into vertical cantilever and horizontal beams so that it can be converted into a determinate beams . After this rest of this will be solving of algebraic equations only.

As in similar manner, for structural dynamics,you are dealing with second order liner differential equations and after getting response at any instant of time as a maximum displacement, velocity & acceleration for dynamic loading or initial displacement to the structure, your work become simple because after that you are only doing static analysis and your structure analysis becomes a static problem.

This is the Series-1 for fixed end moments calculation for central point loads and i will be coming with varieties of loading pattern in a single span fixed beam to find out it’s fixed end moments.

You need to understand the concept of fixed end moments because during analysis of beams and frames using slope deflection methods and moment distribution methods, it is essential to know the quickest method to find out the fixed end moments.

Please download pdf for the calculation of fixed end moments for central point load for a single span fixed beam

Thanks

Mohammad Sohel Akhtar(Structural Engineer), Delhi, India

ANALYSIS OF CONTINUOUS BEAM WITH OVERHANG BY MOMENT DISTRIBUTION METHOD (MDM)

Series-V, Example-1

Here you all civil and structural engineers are invited to go through and download for analysis of two span continuous beam with overhang by moment distribution method. Shear force diagram(SFD) and bending moment diagram (BMD) has been drawn. Two method, loading diagram and conventional method has been used for drawing BMD with greater ease. Also, every steps has been explained fully to understand whole concept.

Please download from here the attached pdf for the analysis for continous beam with overhang by MDM.

Download pdf for the same example in colored format

Same lecture explained through video can be downloaded through below link:

https://youtu.be/27kEBMhBXsk

Thanks & regards.

MSA

HOW EARTHQUAKE OCCURS?

Latest earthquake occurred dated on 28.01.2020 in Caribbean cities like Jamaica,Havana,Kingston, Miami indulged me to write on the subject of earthquake occurrence and it’s cause.

This blog will help many laymen to understand the cause behind the occurrence of earthquake. There are different myth behind the earthquake occurrence among different people. Therefore, as a structural engineer, it’s my duty to explain earthquake in a simpler way. There are two disturbance which are geologically proved are solely responsible for seismic activity. One is disturbance at tectonic plate boundaries and other is on the fault planes. Either of the two plays a vital role for any seismic activity which are explained below.

1. Disturbance on Tectonic Plates Boundaries:

Actually all natural or artificial structures are supported over the earth crust. It is the uppermost part of earth.Below this crust,there is layer of earth which is known as mantle. Mantle is further divided in two layer. Upper mantle & lower mantle.There is a layer above upper mantle known as Mohorovicic discontinuity or Moho. This layer “Moho” behaves like a viscous fluid having convective force due to high temperature. Earth crust being a rigid layer float over Mohorovicic discontinuity as Moho is a viscous fluid mass. How earth crust floats over Moho can be clearly understood when it can be correlated with a plate placed over utensil having water continuously boiling over it .Due to convective force of boiling water,plate starts floating it, in the same manner, earth crust floats over Moho being it a viscous fluid generating convective forces. Geological survey of earth has revealed that earth crust has been dived into twelve plates. All these plate are called as Tectonic Plates. All these plates are resting over Moho Discontinuity & moves with respect to each other due to convective force . As the convective forces are highly unsymmetrical and complex, sometime it exerts force to earth tectonic plate to make it move towards each other or sometime it exerts force on tectonic plate to make plates departs from each other. This process of colliding of one plate with other is convergence while departing of plates with respect to other is called divergence of plates. When two plates collides with each other, then huge amount of energy is released in the form of seismic waves. This release of high energy in the form of wave is called as Seismic Wave. When this wave strike to the structures, it exerts forces on the structure due inertia which is known as Seismic Forces. When two tectonic plates move away from each other, then volcanic eruption takes place in which molten Magma comes out on the earth crust. As this volcanic eruption is vigorous, it also produce vibration to the ground but is not much significant as compared to the earlier case when two plates collide with each other.

2. Disturbance at Faults Plane

Below the earth surface, there are many rocks which are in distorted or in fractured form. These fractures are formed as result of high pressure. These fractures are in unstable condition. When two parts of rocks have relative movement or deformation or dislocation then there is release of large amount of energy in the form of seismic waves. As there are many form of plate tectonic movement like convergence or divergence in vicinity of plate boundaries, in the same way different names of distortion in rock through fault boundaries are named based on the relative movement like Strike -Slip faults, Dip-Slip faults, normal faults or reverse faults. I invite you to learn more through these terms. Please read other literature for thorough knowledge of seismology.

Thanks & regards!

Mohammad Sohel Akhtar

(Structural Engineer)

ANALYSIS OF A TWO EQUALLY SPAN CONTINUOUS BEAM LOADED SYMMETRICALLY BY MOMENT DISTRIBUTION METHOD(SERIES-IV)

Here you will find a very interesting example on two span continuous beam by moment distribution method. Both spans are symmetrically loaded.

In many buildings frames, this example will help you to solve many continuous beam manually .However, five pages have used to solve this problem, but it can be solved in a single page. I have elaborated to make concept clear.

Please find pdf for the example on MDM for two span continuous beam

DOWNLOAD EXCEL SHEET FOR THE DESIGN OF BOLTS & CONNECTION PLATE BETWEEN COLUMN & RAFTER

“This blog will help you to design connection between column & rafter with the customized excel sheet.It will help you to take design output very fast”.

Feel the structure-MSA

For designing steel structures, design of connection plates and bolts and welding are essential part.Normally, in pre-engineered or conventional steel building, we have to assemble structural steel members at site, so we have to fabricate column and rafter separately at workshop providing connection plate at the face of column and rafter. These connection plates have appropriate holes for bolts.Column and rafter are assembled at site by tightening bolts. Therefore, as a structural engineer, we have to design the the thickness of connection plates, size of plates having number of bolts with diameter.

After analysis of any building manually or using any software like STAAD, ANSYS, we need to take reactive forces like shear, axial force and moments. Here in this blog, you need to put the reactive forces in the attached excel sheet in the highlighted areas. Results for thickness of connection plate and bolt diameter with numbers will come automatically in the same sheet.

Please find here design excel sheet for connection plate & bolts between column & rafter as per IS:800(2007) from the below link.

Download Excel Sheet For the Design of Connection Plate & Bolts Between Column to Rafter as per IS:800-2007.

Thanks

Mohammad Sohel Akhtar(MSA)

(Structural Engineer)

DOWNLOAD EXCEL SHEET FOR THE DESIGN OF BOLTS & CONNECTION PLATE BETWEEN RAFTER TO RAFTER

“This blog will help you to design connection between rafter to rafter with the customized excel sheet.It will help you to take design output very fast”.
Feel the structure-MSA

For designing steel structures, design of connection plates and bolts and welding are essential part.Normally, in pre-engineered or conventional steel building, we have to assemble structural steel members at site, so we have to fabricate column and rafter separately at workshop providing connection plate at the face of rafter and rafter. These connection plates have appropriate holes for bolts.Column and rafter are assembled at site by tightening bolts. Therefore, as a structural engineer, we have to design the the thickness of connection plates, size of plates having number of bolts with diameter.

Please download here the excel sheet for the connection plate & bolt between rafter to rafter as per IS:800(2007).

Download Excel Design Sheet for the design of Connection Plate & Bolts Between Rafter To Rafter as per IS:800-2007

Thanks

Mohammad Sohel Akhtar(MSA)

(Structural Engineer)



DOWNLOAD EXCEL SHEET FOR THE DESIGN OF PINNED BASE ANCHOR BOLT & BASE PLATE

“This blog will help you to design base plates /anchor plates and anchor bots for pinned base connection with the customized excel sheet.It will help you to take design output very fast”.

For designing steel structures, design of connection plates and bolts and welding are essential part.Normally, in pre-engineered or conventional steel building, we have to assemble structural steel members at site, so we have to fabricate column with connection plate at it’s bottom at workshop.These columns with connection plates at it’s bottom is assembled with the anchor bolts or fastener which are properly placed at the top of concrete pedestal at site. Therefore, as a structural engineer, we have to design the the thickness of connection plates,base plates & it’s sizes having number of bolts with diameter.

Here you all civil and structural engineers are invited to download excel sheet for the design of pinned base anchor bolt & base plate as per IS:800(2007).

Download excel sheet for the design of pinned base anchor bolt & base plate as per IS:800-2007

Thanks

Mohammad Sohel Akhtar(MSA)

(Structural Engineer)

DOWNLOAD EXCEL SHEET FOR THE DESIGN OF FIXED BASE ANCHOR BOLT & BASE PLATE

“This blog will help you to design base plates /anchor plates and anchor bots for fixed base connection with the customized excel sheet.It will help you to take design output very fast

For designing steel structures, design of connection plates and bolts and welding are essential part.Normally, in pre-engineered or conventional steel building, we have to assemble structural steel members at site, so we have to fabricate column with connection plate at it’s bottom at workshop.These columns with connection plates at it’s bottom is assembled with the anchor bolts or fastener which are properly placed at the top of concrete pedestal at site.For Fixed base connection, stiffeners are provided with the base plates whereas in pinned base connection, no stiffeners are provided. Therefore, as a structural engineer, we have to design the the thickness of connection plates,base plates, stiffener with it’s thickness & it’s sizes having number of bolts with diameter.

All Structural Engineers and students perusing civil engineering are invited to download excel design sheet for anchor base plate & bolts for fixed base connection as per IS:800(2007).

Download Design Excel sheet for the design of fixed base anchor bolt & base plate as per IS:800-2007

Thanks

Mohammad Sohel Akhtar(MSA)

(Structural Engineer)



LIQUEFACTION OF SOIL- A BIG CHALLENGE & CONCERN FOR STRUCTURAL ENGINEER

“Even a sound and structurally stable structure is susceptible to failure if soil supporting structure undergoes liquefaction during earthquake. This is one of the biggest challenge for structural engineer. Reading carefully and attentively the geo-technical report and providing robust foundation or soil improvement is the only solution for this challenge.For solution, it is essential to know what is liquefaction and how does it happens. Without knowing the complete anatomy behind liquefaction,a suitable solution can never be found.

Feel the structure-MSA

As a structural engineer, we design foundation on the basis of data provided by geo-technical consultant. Whatever is the number of bore hole and SPT test done at the site, water table is mentioned in the report for each borehole. Also,soil type is clearly  mentioned in the report. If the soil type is fully sandy or sandy and silty type(SM Type) and water table is high, then in this case, soil has a tendency to liquefy when earthquake occurs. 

Even a sound and structurally stable structure is susceptible to failure if soil supporting structure undergoes liquefaction during earthquake. This is one of the biggest challenge for structural engineer. Reading carefully and attentively the geo-technical report and providing suitable foundation or soil improvement is the only solution for this challenge.For solution, it is essential to know what is liquefaction and how does it happens. Without knowing the complete anatomy behind liquefaction,a suitable solution can never be found.

Generally shallow foundation is provided at a depth of 1.5 m to 2.5 m below natural ground level(NGL).If water table is very highy, say  water table level is 1.5 to 2 m below NGL, then soil in this region is fully submerged condition. And if soil in this region is cohesion less i.e fully Sandy or Sandy -Silty type(SM Type) then whole soil in this region will undergo in liquefaction i.e soil will behave like a fluid and will have shearing strength zero. Liquefaction state of soil is analogue to fluid in terms of shearing strength. As fluid has zero shearing strength,hence soil in the state of liquefaction may have some shearing strength or has zero shearing strength depending upon the liquefaction potential of the soil.You can relate this with an example,when you try to put your hand into the bucket  full of  water, you will feel negligible resistance as a shear by water.In the same manner, when soil is liquefied, then it does not respond any shearing resistance  to the force exerted by the footings supported on it.Hence, in this case structure starts settling/sinking during liquefaction.As liquefaction is not uniform below each footing, hence differential settlement occurs and  due to this building may partially or as a whole may  collapse depending on the liquefaction potential of the soil.Although structural elements of building may or may not have damaged during earthquake but excessive sinking may lead to building non functional.Not only building, even a light weight car can sink when it is standing over liquefied soil because soil is not any potion to  support any loads in liquefaction state.

How Liquefaction Occurs:

To take precautionary action before construction on a site having liquefied soil or doing retrofitting of a damaged building over liquefied soil after earthquake, we need to understand the complete anatomy behind the occurrence of liquefaction of soils during earthquake. 

                 Saturated  cohesion less soil(Sandy or Sandy+Silty) is susceptible to liquefaction during earthquake.Soil under foundation and it’s vicinity is under extremely stressed condition. If soil is saturated,there will be pore water pressure which keep soil particles together. But when earthquake occurs, it produces extreme vibration/turbulence/shaking to the soil particles.This extreme vibrations increases the pore water pressure and also soil gets loosely packed  giving a path to water to flow upwards.As we know, there is always a tendency to flow fluid from high pressure to low pressure.As there is low pressure at the ground, hence water will start flowing from below to ground floor.In this case, voids will be created at the displaced water particle position.In the vicinity of these created voids,loosened/loosely packed soil particles  start moving to fill these voids.Due to this, sinking of soil starts taking place.As the soil supporting structure starts sinking, hence structure also starts sinking. This phenomenon happens in such way, it seems structure is supported over fluid which does not have any shearing strength. This sinking can be from cm to meter. As the turbulence/vibration occurs differently in different foundation system, hence it leads differential settlement.Building may tilt excessively or may collapsed depending upon the liquefaction potential of the soil.

Serious notes to keep in mind for Soil prone to liquefaction: 

This blog will motivate structural engineer to study thoroughly key areas of the Geo-technical report such as the soils types, N-values & water table before designing any foundation.Geo-technical consultant may or may not provide you a statement about whether soil is susceptible to  liquefy or not. Knowing the soil types and water table, you have to understand whether soil will liquefy or not.I have noticed one thing, most of the people are only concerned about the safe bearing capacity(SBC).Sometimes, even structural engineer focuses on SBC only without knowing the soil characteristics like type of soil,N-values, soil compactness like loose,medium dense or highly dense. It is surprising to note, a soil having high potential to liquefy  may have satisfactory safe bearing capacity such as 100 KN/m2 or 120 KN/m2. If somebody design isolated foundation with this data then foundation system may collapse during earthquake.

In recent past, i have gone through the foundation design of an industrial shed proposed at Nepal for Steel Melting Shop(SMS) & Rolling Mill. In Geo-technical report, there was SBC mentioned as 120KN/m2 having average N-values as 10 at a depth of 2.0m. But there was a warning in this report highlighted as soil upto a depth of 4.0 m is prone to liquefy. I talked to Geo-technical consultant regarding the same and drew his attention that isolated foundation will not be safe. He re-analysed the soil characteristics and recommended pile foundation for the same. Raft foundation is also an alternate solution for soil prone to liquefy as it some how stops water to come out above the foundation as it blocks all possible path of water to come from below during excessive shaking in earthquake.

 

Thanks

Mohammad Sohel Akhtar(MSA)

(Structural Engineer)



MYTH AMONG LAYMAN,CONTRACTOR & ARCHITECT PREFERRING USING OF HIGHER REINFORCEMENT & LOWER SIZES OF COLUMN & BEAMS IN RCC BUILDINGS.

” This blog is dedicated to all clients, contractors ,architects and layman who think a RCC building can be make structurally sound using more reinforcement and lesser cross section of structural elements”.

Usually i come across various person like clients, contractors, architects and layman who say, can we reduce the size of column and beam by using higher reinforcement. Actually architects always want very light section which do not affect the beauty of the buildings. As per the structural requirement,when a structural engineer provide a big column or beam then architect says, why not we are using column and beams of lesser cross section by providing higher reinforcement. Occasionally, i have also heard an architect requesting for reducing the beam depth by increasing the depth of the slab or reducing the beam depth by increasing the reinforcement or reducing the depth of beam by increasing the width of beam.

This is an absolutely a wrong perception developed by an architect, contractor and layman.As they are not aware of the role of stiffness for deflection,durability and crack control,they are right for what their perception allow in this subject.Actually, a myth has developed in their mind that if higher reinforcement is used, then structural members will have higher strength.

Also, it was very strange when i came across a person who was suggesting me to put more reinforcement in slab. Actually, one of slab was having reinforcement of 8 mm diameter but our client was insisting me to provide 10 mm diameter reinforcement. Although i tried to convince him that using 8 mm diameter reinforcement is sufficient for that slab but he was not convinced. Then i tried to understand, what does he thinks about structure. After a quality discussion with him on the subject of structural analysis, i realized that he has developed a misconception that slab is one of the most important element in a building as everything is kept on slab. This is not the only case. I have also heard the same by few other people. Therefore, i realized that i have to educate more and more people and will have to bring all people out from this disastrous myth.

It pains me a lot and very unfortunate to state that how people misinterpret things on structural stability and strength on their own way.I am not exaggerating if many buildings have collapsed or severely damaged in recent past by taking very slender column considering only gravity loading. It is amazing to see builder proposes random column sizes as 230 x 230 mm,300 x 300 mm or 230 x 350 mm for three to four storey building without knowing the consequences of heavy gravity loading and earthquake loading. If somewhere , any building with these kind of proposed sizes are safe for gravity loading then it is taken granted same in other places too.I don’t know what will happen to these building for earthquake loading when it will exposed to.It is essential to keep in mind,during earthquake,severity of shaking in two building will be felt differently at the same site due to geometrical differences although both buildings have same number of floors. In the same site,a highly irregular building will feel higher intensity of shaking whereas a regular building will feel less intensity of shaking. Hence, column sizes can not be same in the two buildings however column spacing and floors are same.Actually, reason is that,a highly irregular building will have twisting/torsion in earthquake requiring bigger column sizes to counter twisting whereas highly regular and symmetrical building will have column of lesser cross section as it will not have torsion/twisting.Here, i am not going to elaborate the cause of torsion like difference in Center of rigidity(CR) & Centre of mass(CM).Please read other article related to the same for knowledge.

Actually architects,layman or builders in order to find large spaces for parking or hiding /concealing column in the masonry walls for aesthetics purposes or to get more free spaces for bed room /living room , slender columns are proposed ignoring large span.They can go for beam with more cross sectional area for large span than column.They do not know the concept of strong column and weak beam.Also, they do not know the failure mechanism.And of course, how they will know these very general and basic concept if we do not educate them.

And when they construct a building on their one way without consulting a structural engineer then something very unfortunate happens to human lives and economy.Therefore, our responsibility plays a important role to spread awareness and to stop building collapsing even under gravity loading.

I have noticed that layman, architects & builders think in unidirectional way. The way their perception allows. They think gravity loading is the only loading that is most likely to occur on a building ignoring a large part of seismic loading.They think if building seems safe in gravity loading then it looks fine to them.They seem relaxed and fully unaware of earthquake loading.They do not know column is weak for lateral loads(Seismic/Wind) and strong in compression.

As a structural engineer, it is our responsibility to guide and educate them.Although we will not be able to teach whole civil engineering to them but we should deliver a general concepts to stop tragedy in future. We should make them aware that however we should make building safe for gravity loading but at the same time we should not forget the bigger and serious concern of earthquake loading.Instead of creating havoc, fears and confusion to understand the complex mathematical modeling like numerical methods(differential equations) of physical phenomena of earthquake, we should come up with very simple examples to clear basic concepts of earthquake. We should relate the drifting or lateral deflection of the building when subjected to earthquake forces with the best and easiest example with newton first law of motion.As we know, when a car starts moving then passenger sitting in back seat feel backward push due to concept of newton’s first law of motion or law of inertia.In the same manner, when earthquake forces exerts in the building, then due to inertia,building will try to drift in opposite direction to earthquake force. We should tell them, column should be able to take huge lateral loads and it should be much stiffer than beam to follow the rules of strong column and weak beams.Also, in case of double and triple height column,column should have larger cross section or will have to be tied at different level to stop column failing in buckling.We should demonstrate them the simple concept of bucking failure with simple example by pushing two measuring scale. Say,one scale of length 10 cm and another one of 30 cm.If both of them is pushed by hand,undoubtedly scale of longer length will buckled more as compared with smaller one.These demonstration will help them the concept behind using stiffer column.After reading this article they will come out of the box like thinking that slab is most important part of building as everything supports on slab.They will really come out of this disastrous myth. This blog will help them a lot to understand basic concept of structural analysis.This will help them to understand , however building shall be safe for gravity loading but it is mono-maniacally designed for seismic loading.

Thanks

Mohammad Sohel Akhtar(MSA)

(Structural Engineer)