Analysis of Non-Sway type Portal Frame by Kani's Method (Rotation Contribution Method)

 Analysis of Non-sway type portal frame by Kani's Method (Rotation Contribution Method)

(Initially fixed end moments are obtained by considering Support as fixed and individual member as a fixed beam,

So for Member AB and CD it doesn't carry any type of loading hence Moments are taken as zero.

And the member BC carries udl of 100kN/m over its span of 6m, hence FEM in BC are obtained by using equation M^ab=M^bc=wL2/12)

RCC Columns Subjected to uniaxial bending along with axial loading (Steel Calculation by SP16)

Subject: Structural Engineering-II (RCC) / DOS-II(RCC)

Module 05: Analysis & Design of Column

Topic:- Columns Subjected to Combined axially loaded along with uniaxial bending

        Here in this example height (unsupported length) is not given and so its assumed that moment is due to minimum eccentricity is less than the actual moment.

        If in case height (unsupported length) is known, have to check slenderness of column as well as minimum eccentricity too.

Use of SP:16 for calculation of reinforcement on two opposite sides by using charts 

Number of bars obtained as above are to be arranged equally on to opposite faces i.e, 5 Nos on each face.

Use of SP:16 for calculation of reinforcement on four sides by using charts

Number of bars obtained as above are to be arranged equally on all faces i.e, 4 Nos on each face.

Simple Numerical on Shear Stresses in Beams Part-II (SOM)

 

Shear Stresses in Beams

Numerical #02: An I—section beam of size 350 mm x 150 mm has a web of thickness 10mm and a flange of thickness 20 mm. Find the maximum Shear Stress developed in the I-section, if the shear force acting on the section is 40 kN.

Simple Numerical on Shear Stresses in Beams Part-I (SOM)

further in the above numerical if it has asked to find average shear stress in the section then, can be found as,

Avg. Shear stress = Shear Force/ Cross-sectional Area

Avg. Shear Stress = 4500 /(100*150) = 0.30 N/mm2

And as we know maximum shear stresses will be at NA, and it can be alternatively found as, Max. Shear Stress = 1.5*Avg. Shear Stress

Max. Shear Stress = 1.5*0.30 = 0.45 N/mm2

Shear Stress Distribution across the section will be parabolic, as shown in fig.

Introduction to Concrete Technology Part-II (Cement)

 Introduction to Concrete Technology Part-II (Cement)

By Md. Yousuf Shaikh Ameer

Assistant Professor

Hydration of cement

·   When Portland cement is mixed with water its chemical compounds undergoes a series of different chemical reactions that cause it to harden. This chemical reaction with water is called "hydration". Every reaction occurs at a different time and rate. Together, the results of these reactions show how Portland cement hardens and gains strength.

 

OPC hydration

Hydration starts as soon as the cement and water are added and mixed.

·         The rate of  heat of hydration and the heat emmitted by the reaction of each compound is different

           ·         Each compound goes under different reactions and produces different products when it hydrates.

·         Tri-calcium silicate (C₃S). Hydrates and hardens rapidly and is wholly responsible for initial set and early strength of cement. Portland cements with higher percentages of C₃S will gain high early strength.

·         Tri-calcium-aluminate ( C₃A). Hydrates and hardens the quickest. Liberates a large amount of heat almost immediately after mixing and contributes somewhat to early strength. Gypsum is added to Portland cement to retard the amount of C₃A hydration. Without gypsum, due to C₃A Hydration it causes Portland cement to set as quickly after adding water.

·         Di-calcium silicate (C₂S). Hydrates and hardens slowly and is mainly responsible for strength increases beyond one week.

·         Tetra-calcium-alumino-ferrite (C₄AF). Hydrates rapidly but contributes very little to strength. By using it allows lower kiln temperatures in Portland cement manufacturing. Most of the Portland cement color effects are due to C₄AF.

Heat of Hydration

·         The heat of hydration is the heat evolved when water and Portland cement react. Heat of hydration is mostly influenced by the proportion of C₃S and C₃A in the cement but is also influenced by water-cement ratio, fineness and curing temperature. As any one of these factors is increased, heat of hydration increases.

·         For usual range of Portland cements, about one-half of the total heat is emmited between 1 and 3 days, about three-quarters in 7 days, and nearly 90 percent in 6 months.

           ·         The heat of hydration of cement depends on the chemical composition of cement.

Physical Properties of OPC and their tests

·         Portland cements are commonly checked by their physical properties for quality control purposes. Its physical properties can be used to classify and compare Portland cements. Now the challenge in physical property characterization is to develop physical tests that can satisfactorily characterize key parameters.

The physical properties of cement

 

·           Setting Time

·           Soundness

·           Fineness

·           Strength

 

Fineness:

 

·      Fineness of cement mostly refers to the size of grains or particles of cement. Lesser the grain size, finer the cement. Due to small grain size, more surface area is available for contact with water and hence the reaction of hydration becomes very faster, gaining of strength is more rapid and rate of evolution of heat increases.

Test for Fineness                                                                                                            

There are two methods prescribed in IS code for testing of fineness.

I)     Sieve Test (IS 4031, part 1 1996):

II)   Air permeability Method (IS 4031, part 2 1999)

 

Sieve Test (IS 4031, part 1 1996):

This is very simple test. The procedure is given below

 

·         Weight 100 gram of cements correctly and takes it on a standard IS sieving number 9, i.e. a sieve size 90 microns.

·         Break down if any air set lumps found in the sample with fingers.

·         Continuously sieve the sample giving circular and vertical motion for a period of period at least 5 minutes. Mechanical sieving device may also be used.

·         Weigh the residue left on the sieve.

·         This residue shall not exceeds by the limits given as per IS CODE below

·         OPC                                        10 gm 

       Rapid Hardening Cement         5gm

Air permeability Method (IS 4031, part 2 1999)

·        In this method, the permeability of a cement  bed for passage of air current is released with the specific surface of the grains of cement.

·         The finer the grains, the more the specific surface.

·       Lea and nurse permeability apparatus is used for the test, which is shown in below fig. the diameter of permeability cell is 2.5 cm.

·         knowing the density of cement the weight of cement required to make a cement bed of 0.47 porosity can be calculated. The procedure of the test is given below.

·        Fill the weight of cement as calculated above for making a bed of 0.475 porosity into the permeability cell.

·         Slowly slowly pass dry air through the cement bed at a constant velocity

·         Read the difference in manometer limbs and note it h₁

·         Read the difference in flow meter limbs and not it has h₂. It should be between 30 to 50 cm.

·         Repeat the readings untill steady state is achieved.

·         Specific surface is calculated by following formula

 

K = √Ɛ³A/CL

Where     Ɛ     = Porosity =0.475

L    = length of cement bed (cm)

D    = density of cement in gm/cm³ C             = flow meter constant.

A     = Area of c/s of cement bed (cm²)

Generally value of C and K are provided be the manufacturer for different value of porosity.

·         This specific surface should not be less than the limits given below. OPC: Not less than 2250 cm²/gram

Rapid hardening cement: Not less than 3250 cm²/gram Low heat Cement: Not less than 3200 cm²/gram.

Setting Time:

Cement paste setting time is influenced by a number of factors including:

·         Cement fineness, water-cement ratio, chemical content (specially gypsum content) , type of cement and admixtures. Setting tests are used to determine how a particular cement paste sets.

·         For construction purposes, the initial setting time must not be too soon and the final settting time must not be too late.

Normally, two setting times are define:

1)      Initial setting: Occurs when the paste begins to stiffen considerably and when cement will lose its plasticity.

2)      Final stetting: Occurs when the cement has hardened to the point at which it can sustain some load.