Wednesday, April 13, 2016

Test of Initial & Final Setting Timef

INITIAL & FINAL SETTING TIME
We need to calculate the initial and final setting time as per IS: 4031 (Part 5) – 1988. To do so we need Vicat apparatus conforming to IS: 5513 – 1976, Balance, whose permissible variation at a load of 1000g should be +1.0g, Gauging trowel conforming to IS: 10086 – 1982.

Procedure to determine initial and final setting time of cement
i) Prepare a cement paste by gauging the cement with 0.85 times the water required to give a paste of standard consistency.
ii) Start a stop-watch, the moment water is added to the cement.
iii) Fill the Vicat mould completely with the cement paste gauged as above, the mould resting on a non-porous plate and smooth off the surface of the paste making it level with the top of the mould. The cement block thus prepared in the mould is the test block.

A) INITIAL SETTING TIME
Place the test block under the rod bearing the needle. Lower the needle gently in order to make contact with the surface of the cement paste and release quickly, allowing it to penetrate the test block. Repeat the procedure till the needle fails to pierce the test block to a point 5.0 ± 0.5mm measured from the bottom of the mould.The time period elapsing between the time, water is added to the cement and the time, the needle fails to pierce the test block by 5.0 ± 0.5mm measured from the bottom of the mould, is the initial setting time.

B) FINAL SETTING TIME
Replace the above needle by the one with an annular attachment. The cement should be considered as finally set when, upon applying the needle gently to the surface of the test block, the needle makes an impression therein, while the attachment fails to do so. The period elapsing between the time, water is added to the cement and the time, the needle makes an impression on the surface of the test block, while the attachment fails to do so, is the final setting time.

Thursday, April 7, 2016

Stress and Deflections of Beams


The calculator below can be used to calculate maximum stress and deflection of beams with one single or uniform distributed loads.

Beam Supported at Both Ends, Uniform Load

beam stress deflection uniform load

Maximum Stress


beam flange
Maximum stress in a beam with uniform load supported at both ends can be calculated as
σ = y q L2 / (8 I)         (1)
where
σ = maximum stress (Pa (N/m2), N/mm2, psi)
y = Distance of extreme point off neutral axis (m, mm, in)
q = uniform load per length unit (N/m, N/mm, lb/in)
L = length of beam (m, mm, in)
I = moment of Inertia (m4, mm4, in4)
  • 1 N/m2 = 1x10-6 N/mm2 = 1 Pa = 1.4504x10-4 psi
  • 1 psi (lb/in2) = 144 psf (lbf/ft2) = 6,894.8 Pa (N/m2) = 6.895x10-3 N/mm2
Maximum deflection can be expressed as
δ = 5 q L4 / (E I 384)         (2)
where
δ = maximum deflection (m, mm, in)
E = modulus of elasticity (Pa (N/m2), N/mm2, psi)
Note! - deflection is often the limit factor in beam design. For some applications beams must be stronger than required by maximum loads, to avoid unacceptable deflections.

Example - Beam with Uniform Load, Metric Units

A beam with length 5000 mm carries a uniform load of 6 N/mm2. The moment of inertia for the beam is 78125000 mm4 and the modulus of elasticity for the steel used in the beam is 200000 N/mm2. The height of the beam is 300 mm (the distance of the extreme point to the neutral axis is 150 mm).
The maximum stress in the beam can be calculated
σ = (150 mm) (6 N/mm2) (5000 mm)2 / (8 (78125000 mm4))
  = 36 N/mm2
  = 36000000 N/m2 (Pa)
The maximum deflection in the beam can be calculated
δ = 5 (6 N/mm2) (5000 mm)4 / ((200000 N/mm2) (78125000 mm4) 384)
   = 3.13 mm

Uniform Load Beam Calculator - Metric Units

q - Uniform load (N/mm)
L - Length of Beam (mm)
I - Moment of Inertia (mm4)
E - Modulus of Elasticity (N/mm2)
y - Distance of extreme point off neutral axis (mm)
  • 1 mm4 = 10-4 cm4 = 10-12 m4
  • 1 cm4 = 10-8 m = 104 mm
  • 1 in4 = 4.16x105 mm4 = 41.6 cm4
  • 1 N/mm2 = 106 N/m2 (Pa)

Uniform Load Beam Calculator - Imperial Units

q - Load (lb/in)
L - Length of Beam (in)
I - Moment of Inertia (in4)
E - Modulus of Elasticity (psi)
y - Distance of extreme point off neutral axis(in)

Example - Beam with Uniform Load, English Units

The maximum stress in a "W 12 x 35" Steel Wide Flange beam, 100 inches long, moment of inertia 285 in4, modulus of elasticity 29000000 psi, with uniform load 100 lb/in can be calculated as
σ = y q L2 / (8 I)
    = (6.25 in) (100 lb/in) (100 in)2 / (8 (285 in4))
    = 2741 (lb/in2, psi)
The maximum deflection can be calculated as
δ = 5 q L4 / (E I 384)
    = 5 (100 lb/in) (100 in)4 / ((29000000 lb/in2) (285 in4) 384)
    = 0.016 in

Beam Supported at Both Ends, Load at Center

beam stress deflection single load

Maximum Stress

Maximum stress in a beam with uniform load supported at both ends can be calculated as
σ = y F L / (4 I)         (3)
where
σ = maximum stress (Pa (N/m2), N/mm2, psi)
y = Perpendicular distance from to neutral axis (m, mm, in)
F = load (N, lb)
L = length of beam (m, mm, in)
I = moment of Inertia (m4,mm4, in4)
Maximum deflection can be expressed as
δ = F L3 / (E I 48)         (4)
where
δ = maximum deflection (m, mm, in)
E = modulus of elasticity (Pa (N/m2), N/mm2, psi)

Single Center Load Beam Calculator - Metric Units

F - Load (N)
L - Length of Beam (mm)
I - Moment of Inertia (mm4)
E - Modulus of Elasticity (N/mm2)
y - Distance of extreme point off neutral axis (mm)

Single Center Load Beam Calculator - Imperial Units

F - Load (lb)
L - Length of Beam (in)
I - Moment of Inertia (in4)
E - Modulus of Elasticity (psi)
y - Distance of extreme point off neutral axis (in)

Example - Beam with a Single Center Load

The maximum stress in a "W 12 x 35" Steel Wide Flange beam, 100 inches long, moment of inertia 285 in4, modulus of elasticity 29000000 psi, with a center load 10000 lb can be calculated like
σ = y F L / (4 I)
    = (6.25 in) (10000 lb) (100 in) / (4 (285 in4))
    = 5482 (lb/in2, psi)
The maximum deflection can be calculated as
δ = F L3 / E I 48
    = (10000 lb/in) (100 in)3 / ((29000000 lb/in2) (285 in4) 48)
    = 0.025 in

Some Typical Vertical Deflection Limits

  • total deflection : span/250
  • live load deflection : span/360
  • cantilevers : span/180
  • domestic timber floor joists : span/330 (max 14 mm)
  • brittle elements : span/500
  • cr

Structural Beam Deflection Equations and Stress Formula and Beam Deflection Calculators

Structural Beam Deflection and Stress Formula and Calculation: The follow web pages contain engineering design calculators will determine the amount of deflection a beam of know cross section geometry will deflect under the specified load and distribution. Please note that SOME of these calculators use the section modulus of the geometry cross section of the beam. You will need to determine the moment of inertia of the cross section and the distance from the neutral axis to the edge of your geometry.
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Circular plate, uniform load, edges simply supported equation and calculator.
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Rectangular plate, uniform load, simply supported equations and calculator
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Circular Cantilever Beam in Direct Compression and Bending
Combined Stress Circular Cantilever Beam in Direct Compression and Bending Equations and Calculator
Circular Cantilever Beam in Direct Tension and Bending Equations and Calculator 
Rectangular Cantilever Beam in Direct Compression and Bending Equations and Calculator
Rectangular Cantilever Beam in Direct Compression and Bending Equations and Calculator
Rectangular Cantilever Beam in Direct Compression and Bending Equations and Calculator
Combined Loading on Circular Beam or Shaft in Direct Compression and Bending Equation and Calculator
Combined Loading on Circular Beam or Shaft in Direct Compression and Bending Equation and Calculator
Combined Loading on Circular Beam or Shaft in Direct Tension and Bending Equation and Calculator
Cored Laminate Composite Stiffness Calculator
W-Flange Overhead Monorail Beam Analysis Calculator
S-Flange Overhead Monorail Beam Analysis Calculator
K-Series Joist Deflection and Stress Analysis Calculator
Davits
Davits refer to single mechanical arms with a winch for lowering and raising objects. A davit is commonly used systemto used to lower an emergency lifeboat from a ship to the embarkation level to be boarded.
Principal and Von-Mises Stress Equations and Calculator
Principal stresses for 2 dimensional plane stress system and von-mises stress equations and calculator.
MOhr's Circle
Mohr's Circle Equation and Calculator
Mohr's circle is a geometric representation of the 2-D transformation of stresses.
NOTE: Large webpage that opens in pop-up window.
Section Modulus
Fixed Pin Cantilever Beam Design
Plate Deflection & Stress
Axial Load Capacities Single Plates Calculator
Tapered BEam Deflection Stress
Concrete Rectangular Beam Section Analysis Calculator
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Bolt Shear
Eccentric Loading On Bolt Group One Vertical Row Calculator
Eccentric Loading On Bolt Group One Vertical Row Calculator - Based on the Instantaneous Center of Rotation Method and Alternate Method 2, Using Table XI from AISC 9th Ed. Manual (ASD) - page 4-62
Eccentric Loads on Bolt Groups for Two Vertical Rows of Bolts Based on the Instantaneous Center of Rotation Method and Alternate Method 2 Using Table XII from AISC 9th Ed. Manual (ASD) - page 4-63
/calculators/bolt-group/BOLTGRPXIII/bolt-grp-xiii.htm
Eccentric Loading on Bolt Pattern for Vertical Rows of Four Based on the Instantaneous Center of Rotation Method and Alternate Method 2 Using Table XVII from AISC 9th Ed. Manual (ASD) - page 4-68
Column Bucking
Pressure Vessel
Stress Concentration
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Bolt or Pin Single Shear Equation and Calculator
Bolt or Pin Single Shear Equation and Calculato