Lecture -07 Misc topics.ppt

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Effect of Residual stresses on tension members
Topics to be Addressed
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similar to that of tensile-test coupon .
Member behavior may differ from coupon
behavior because of:
Non-linear behavior of connections
Residual stresses in member
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Residual Stresses
Residual stresses result principally from non-uniform cooling of hot rolled or welded shapes and from cold straightening of bent members.
1. Thermal Residual Stresses
CE-409: Lecture 07 Prof. Dr Akhtar Naeem Khan
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Residual Stresses
As they have more surface exposure per unit of volume, flange tips and central parts of the webs tends to cool faster than juncture of flange-web of a section (w-f) i.e. rate of cooling of juncture is slower than rate of cooling of tips
As a result, metal at junctures continues to contract as it cools after flange tips and web interior have cooled to temperature of surroundings.
Thermal Residual Stresses: W /I shape
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This contraction is partially restrained by cooler metal which causes:
Tensile stresses to develop at the juncture of flange-web
Compressive stresses in the remainder of the cross-section
These are called residual Stresses.
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20 W’s shapes were investigated:
It Revealed that flange-tip stress frc varied from 4.1 to 18.7 Ksi, the average being 12.8 ksi
Residual stresses in web center varied from 41Ksi compression to 18.2Ksi tension.
Showing some W’s develop residual tension over entire web, instead the pattern shown.
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Only one out of 20 sections was thicker than 1 in.
Therefore, above values are not representative of W’s with thick flanges and webs
Residual stresses tend to increase in magnitude with increase in thickness
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Two straightening procedures:
Residual stress distribution changes along entire length of member.
Gagging: Concentrated straightening at few points
Almost no change in thermal R.S
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Residual Stresses in welded connection
Because of high concentration of heat, tensile residual stresses at the weld in welded members usually equal the yield strength of the weld metal itself which may be as much as 50% higher than that of the parent metal.
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Magnitude and distribution of thermal residual stresses are influenced to considerable degree by geometry of x-section
Residual stresses tend to increase in magnitude with increase in thickness
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Method of preparation
Large residual stresses develop at the corners of the welded box
On the other hand, residual stresses in the hot-rolled square box are very low and in one investigation averaged less than 5 ksi.
Method of preparation changes the distribution of Residual stresses.
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Fabricating operation
Fabricating operations such as cambering and straightening by cold bending also induce residual stresses.
These are of about the same magnitude but differ in distribution
These stresses are superimposed on the thermal residual stresses.
Method of preparation changes the distribution of Residual stresses.
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Quenching and Tempering
Quenching is the act of rapidly cooling the hot steel to harden the steel.
Quenched steel is hard and brittle.
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Effect of RS on Tension Members
Generally tension members response to load is much similar to that of tensile-test coupon but not identical.
However member behavior may differ from coupon behavior because of:
Slip in bolted & riveted connections
Non-linear behavior of connections
Residual stresses in member
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The section is an idealized (web less) H
Residual-stress distribution is considered as linear
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For Fig (d):
P = 2(24x12x1) = 576kips
favg = 576/24 = 24ksi
A
B
C
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A
B
C
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A
B
C
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No effect on the yield strength of the member
Lowering of proportional limit (P.L <36ksi)
Increase in the strain at initiation of overall yielding
→No consequence in regard to the static strength of the member
→Can be important if fatigue is involved
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Net Section
Holes for bolts or rivets in tension members effect the member in two ways
Reduce area of x-section
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Net Section
Net area is defined as gross section minus area which is lost because of holes.
Effective net area is obtained by multiplying net area by coefficient to account for its reduced effectiveness if not all the member elements are connected.
(According to AISC)
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Net Section: Staggered bolts
Failure paths may occur on sections normal to axis of member (1-2-5) or may include zigzag sections (1-2-3-4).
Depending on the relative values of g, s and bolt diameter d.
g: gauge (distance btw longitudinal fastener line)
s: pitch (distance btw transverse rows)
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If g > s : failure is expected along 1-2-3-4
If g < s : failure is expected along 1-2-5
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Net Section
Empirical methods have been developed to calculate the net section fracture strength
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Net Section
The net width concept is useful when elements of uniform thickness are being evaluated
→ It is called s2t/4g rule.
If the plate thickness is uniform, we can divide each term by ‘t’ to get:
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Net Section
If staggered lines of bolts are present in both legs of an angle, then the net area is found by first unfolding the angle to obtain an equivalent plate.
The unfolding is done at the middle surface to obtain a plate with gross width equal to the sum of the leg lengths minus the angle thickness.
Staggered bolts in angles.
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Staggered bolts in angles.
AISC Specification B2 says that any gage line crossing the heel of the angle should be reduced by an amount equal to the angle thickness.
For this situation, the distance g will be
= 3 + 2 – ½ in.
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Net Section
Example 01
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For line a-b-d-e

For line a-b-c-d-e
wn = 16.0 – 3 (1.125) + 2 x 32/ (4 x 5) = 13.52 in.
The line a-b-c-d-e governs:
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Example 3-6-1. A 7x4x3/4 angle is connected by two rows
of 3/4in Bolts in the 7in leg and one row in the 4in leg
as shown. Standard holes are used.
Determine the pitch s so that only two holes for 3/4in
Fasteners need to be deducted in computing the net area
(b) Determine the net area of the 7x4 angle if the pitch s
is 2in
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Example 02 (a)
The fastener gages shown are the usual values for 7x4 angle.
For section abde: Wn = (7+4-0.75)-2(.75+1/8) = 12
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Example 02 (a)
The fastener gages shown are the usual values for 7x4 angle.
For the section abcde: wn = 10.25-(3x0.875)+s2/(4x3) +s2/(4x4.25)
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S = 2.48in ≈ 2.50in
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= 6.15in2
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( From Gaylord)
Due Date:
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Stresses on Net Section
Consider the non uniform strain in the vicinity of the hole in a
uniformly Stretched sheet of rubber as shown
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The stretched sheet The strains at the edge of the elongated hole are
much larger than those elsewhere in the sheet. The disturbance is highly
localized.
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According to theory of elasticity, the distribution of stress on net section of infinitely wide plate containing a hole at its centerline is given by
f 1 = stress that would exist if there were no hole
r = radius of hole
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As the disturbance in stress is highly localized, this equation can be applied with good accuracy to a plate of finite width.
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Example: Let the plate shown above is subjected to a uniformly distributed tension of 12ksi as shown:
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Tension members do not always develop a net section average stress equal to tensile strength.
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Ratio of gage g to fastener diameter d
Ratio of net area in tension to area in bearing on fastener(Called bearing ratio)
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Net Section efficiency
1.Ductility of metal
Because of non uniform stress distribution efficiency of net section is dependent on ductility of metal.
Net section in highly ductile material may be 15 to 20 % stronger than same section in material with relative low ductility (from test results)
This effect can be expressed by net section efficiency coefficient K1
K1=0.82 + 0.0032R <= 1
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1.Ductility of metal
R: percent reduction in the area of a standard test coupon (2in gage length)
R = 50% or more for A36 steel
→ K1 = 0.98 ≈ 1
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Method of making holes
Punched holes may reduce efficiency of net section by as much as 15% compared with drilled holes.
This effect can be expressed by efficiency coefficient K2.
K2 = 0.85 for punched holes
K2 = 1 for drilled, sub-punched and reamed holes
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g/d ratio
Net section is more efficient if ratio of gage g to diameter d is small than if it is large.
Efficiency coefficient K3 is proposed for this effect.
K3 = 1.6 – 0.7 (An / Ag)
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Net area in tension to area on bearing ratio
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Net area in tension to area on bearing ratio
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The phenomenon of non-uniform straining of web.
Ends of web are free and four forces shows resultants of bolt shear.
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Shear Lag effect
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Effective Net area
The effective area is obtained by multiplying the net area with all the above mentioned coefficients:
Ae = K1 K2 K3 K4 An
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Lecture -07 Misc topics.ppt