ISO 11662-2:2014

INTERNATIONAL ISO
STANDARD 11662-2
First edition
2014-11-01
Mobile cranes — Experimental
determination of crane
performance —
Part 2:
Structural competence under static
loading
Grues mobiles — Détermination expérimentale des performances des
grues —
Partie 2: Compétence structurale sous le chargement statique
Reference number
©
ISO 2014
© ISO 2014
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ii © ISO 2014 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 3
5 Limitations . 5
6 Method of loading . 5
6.1 Suspended load. 5
6.2 Side load (SL). 5
6.3 Deflection criteria . 6
7 Facilities, apparatus, and material . 9
8 Preparation for test . 9
9 Test procedure and records .10
9.1 Final test preparation .10
9.2 Zero stress condition .10
9.3 Dead load stress condition .10
9.4 Working load stress .10
9.5 Overload test condition .11
10 Stress evaluation .11
10.1 Class I — Uniform stress areas .12
10.2 Class II — Stress concentration areas .12
10.3 Class III — Column buckling stress areas .12
10.4 Class IV — Local plate buckling areas .13
Annex A (normative) Strength of materials .14
Annex B (normative) Column buckling stress .17
Annex C (normative) Test conditions and strength margins .24
Annex D (informative) Report format .33
Annex E (informative) Typical crane examples .35
Bibliography .40
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers
to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 96, Cranes, Subcommittee SC 6, Mobile Cranes.
ISO 11662 consists of the following parts, under the general title Mobile cranes — Experimental
determination of crane performance:
— Part 1: Tipping loads and radii
— Part 2: Structural competence under static loading
iv © ISO 2014 – All rights reserved

Introduction
When design calculations are made for mobile cranes, they are based on an ideal model in which all
members and components are perfectly straight and fabrication has been exact. For tension members
and members subjected to bending, the difference between the real crane and the ideal model is usually
not significant. But, for compression members subject to column buckling, an allowance for deviation in
straightness and fabrication is necessary.
When mobile cranes are tested non-destructively by means of strain gauges, the stresses determined
intrinsically include these effects of deviations in straightness and accuracy of fabrication.
This test method is intended to describe the approximate maximum loading conditions to which any
component of the entire load-supporting structure of a crane is subjected (See Annex D). In some
cases, a more severe loading condition(s) can be indicated by analysis. In these cases, the more severe
condition(s) can be added to or substituted for the specified test loading condition(s). This test method
also classifies stress areas as Types I (Uniform Stress Areas), II (Stress Concentration Areas), III (Column
Buckling Areas), and IV (Local Plate Buckling Areas; see Clause 10), and defines limits for each class.
Results can be used to correlate boom system calculation results for Class III stress areas as given by
boom system calculations. Test results for Class I stress areas throughout the structure can be used to
check any available calculations. This test method evaluates Class II stress areas for which calculations
are seldom available. Class IV stress areas, where disproportionately high stress readings can occur, can
be reviewed for better insight by calculation methods.
A production boom system that has been rated by the methods of this part of ISO 11662 can be used
on another machine without re-testing by the methods specified herein, provided the same analytical
procedure shows its stress levels will be less than or equal to the stress levels in the original application,
and provided that the supporting structure is as rigid as the original mounting. Rigidity of the supporting
structure is determined by the change in the slope of the jib foot axis as test loads are applied.
INTERNATIONAL STANDARD ISO 11662-2:2014(E)
Mobile cranes — Experimental determination of crane
performance —
Part 2:
Structural competence under static loading
1 Scope
This part of ISO 11662 applies to mobile construction-type lifting cranes utilizing
a) rope supported, lattice boom attachment or lattice boom, and fly jib attachment (see Annex E,
Figure E.3),
b) rope supported, mast attachment and mast mounted boom, and fly jib attachment (see Annex E,
Figures E.1 and E.2), or
c) telescoping boom attachment or telescopic boom and fly jib attachment (see Figure E.4).
Mobile crane manufacturers can use this part of ISO 11662 to verify their design for the mobile crane
types illustrated in Figures E.1 through E.4.
This test method is to provide a systematic, non-destructive procedure for determining the stresses
induced in crane structures under specified conditions of static loading through the use of resistance-
type electric strain gauges, and to specify appropriate acceptance criteria for specified loading
conditions.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 9373:1989, Cranes and related equipment — Accuracy requirements for measuring parameters during
testing
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
strain
relative elongation or compression of material at any given point with respect to a specific plane passing
through that point, expressed as change in length per unit length (m/m)
3.2
stress
S
internal force per unit area resulting from strain, expressed in pascals (Pa) or newtons/square meter
Note 1 to entry: For this document, megapascals (Mpa) will be used for brevity.
3.3
yield point
S
y
stress at which a disproportionate increase in strain occurs without a corresponding increase in stress
Note 1 to entry: For purposes of this code, yield point is to be considered as the minimum 0,2 % offset tensile yield
point or yield strength specified by the appropriate standard for the material used.
3.4
critical buckling stress
S
cr
average stress which produces an incipient buckling condition in column-type members (See Annex C)
3.5
initial reference test condition
defined no-stress or zero-stress condition of the crane structure after the “break-in” as established by
a) supporting the structure on blocking to minimize the effects of gravity, or
b) the crane structure components in an unassembled state or any alternate method that will establish
the zero-stress condition. Under this condition, the initial reference reading for each gauge is
obtained, N
3.6
dead load stress condition
completely assembled crane structure on the test site and in the position or attitude, ready to apply the
specified live load at the specified radius
Note 1 to entry: Under this condition, the second reading for each gauge is obtained, N .
Note 2 to entry: The hook, hook block, slings, etc. are considered part of the suspended load but may be supported
by the crane when this reading is taken. For dead load purposes, the hook in the “home” position – suspended
from the crane without lifting the test load. This position has to be repeated after placing the load back on the
ground (see 9.4.4).
3.7
dead load stress
S
stress computed as defined in Clause 10 by using the difference in the readings obtained in 3.6 and 3.5
for each gauge (N – N )
2 1
3.8
working load stress condition
completely assembled crane structure on the test site and in the specified position, supporting the
specified rated load
Note 1 to entry: Under this condition, the third reading for each gauge is obtained, N .
3.9
working load stress
S
stress computed as defined in Clause 10 by using the difference in the readings obtained in 3.8 and 3.5
for each gauge (N – N )
3 1
3.10
resultant stress
S
r
stress induced in the structure as a result of dead load stress (S ) or the working load stress (S ),
1 2
whichever is greater in absolute magnitude
2 © ISO 2014 – All rights reserved

3.11
column average stress
S
ra
direct compression stress in a column or the average stress computed from several gauges located at the
section (see Annex B)
3.12
column maximum stress
S
rm
maximum compression stress in a column computed from the plane of buckling as established from
several gauges located at the section (see Annex B)
3.13
loadings
application of weights and/or forces of the magnitude specified under the condition specified
3.14
load radius
horizontal distance between the axis of rotation of the turntable of the crane and the vertical axis of the
hoist line or load block when the crane is erected on a level site
4 Symbols and abbreviated terms
E modulus of elasticity
K effective length factor for a column
L un-braced length of column
L length of boom
b
L length of fly jib
j
L small arbitrary projected length of fly jib along x-axis
L projected length of fly jib strut along y-axis
n strength margin
n strength margin, Class I area, ratio of yield strength to resultant or equivalent stress
n strength margin, Class II area, ratio of yield strength to resultant or equivalent stress
n strength margin, Class III area, derived from an interaction relationship
N strain reading at initial reference test condition
N strain reading at dead load stress condition
N strain reading at working load stress condition
r radius of gyration
RL rated load as specified by manufacturer
“R” plane (Figure 1) perpendicular to boom foot pin centreline (CL)
RR rated radius as specified by manufacturer
S stress
S dead load stress
S working load stress
S column average stress computed from several gauges at a cross section
ra
S critical buckling stress for axially loaded columns
cr
SL side load, i.e. 0,02 × RL;
percentage of side load expressed as a percentage of rated load or %RL = Percentage of
%SL
rated load
SLL side load left
SLR side load right
S maximum compression stress in a column
rm
S stress at the proportional limit
p
S resultant stress
r
S maximum residual stress in compression
RC
S stress at the yield point
y
S’ equivalent uniaxial stress
t horiz. distance from the load centre to the front pad reaction centre for each box jib section
σ tensile yield stress
σ maximum principal stress
x
σ minimum principle stress
y
Z’ lattice boom tip slope (out of plane)
Z lattice boom tip deflection from plane “R”
b
Z fly jib tip deflection from plane “R”
j
Z boom deflection at a point l back from the boom tip
1 1
Z fly jib strut deflection at its tip
α imperfection factor
β fly jib offset angle from centreline (CL) jib
ε strain
ε strain recorded from leg “a” of rosette
a
ε strain recorded from leg “b” of rosette
b
ε strain recorded from leg “c” of rosette
c
ε strain recorded from leg “d” of rosette
d
ε maximum principal strain
x
4 © ISO 2014 – All rights reserved

ε minimum principal strain
y
µ units of strain, 10
θ fly jib tip rotation about x-axis (radians)
π Pi = 3,1416
τ shear yield stress
ν Poisson’s ratio
X relative buckling stress ( = S /S )
cr y
initial relative slenderness
λ
relative slenderness (= λ/λ )
c
λ
slenderness ratio (= KL/r)
λ
 
E
λ reference slenderness ratio =π
 
c
S
y
 
S allowable buckling stress
k
S Euler’s buckling stress
ci
S Jager’s buckling stress
ck
5 Limitations
5.1 This method applies to load-supporting structures as differentiated from power transmitting
mechanisms. It is restricted to measuring stresses under static conditions and a general observation after
overload conditions.
5.2 Personnel competent in the analysis of structures and the use of strain-measuring instruments are
required to perform the tests.
6 Method of loading
6.1 Suspended load
The specified load suspended at the specified radius and held stationary a short distance above the
ground. The weight of the hook, block, slings, etc., shall be included as part of the specified suspended
load.
6.2 Side load (SL)
When the test specification requires side loading, the force displacing the suspended load should
be horizontal and perpendicular to the plane containing the axis of upper structure rotation and
the centreline of the undeflected boom. The side load shall be applied in each direction. Side loading
is applied to simulate the various effects associated with machine operation including a 9 m/s wind
loading that might be encountered.
6.2.1 Lattice boom attachment
For lattice boom attachments, the side load that is to be applied for the conditions listed in Table C2 is as
follows. The side load shall be applied as 2 % (0,02 RL) of the rated load in each direction.
6.2.2 Mast attachments
For mast attachments, the side load percentage that is to be applied in each direction at the load
attachment point for the conditions listed in Table C1 is to be a minimum of 2 % (0,02 RL) of the rated
load in each direction.
6.2.3 Telescoping boom attachment
For telescoping boom attachments, the side load that is to be applied for the conditions listed in Table C3
is as follows. The side load shall be applied as 3 % (0,03 RL) of the rated load in each direction with the
boom over the end of the machine.
6.3 Deflection criteria
The usability of a latticed column [i.e. lattice boom and fly jib(s) combination] or a telescoping boom
attachment is sometimes affected by the elastic stability of the overall column as well as of the individual
members. Incipient out of plane elastic instability is indicated by excessive boom and/or fly jib tip
deflection (sideways) as the attachment is side loaded when suspending a rated load. The following
lateral deflection limits are therefore imposed.
6.3.1 Lattice boom attachments
The lateral deflection criteria for the rated load and side load of Table C2 are as follows. First, the
deflection of the total boom and jib combination shall be less than or equal to 2 % of the total combination
length. Furthermore, the deflection of each individual boom or fly jib member shall be less than or equal
to 2 % of the length of that member. To satisfy these criteria, it should be noted that the deflection of
an individual member does not include the deflection, rotation, or slope of the member to which it is
mounted.
For a single fly jib mounted on a boom, the following relationship is given (Figure 1):
ZL≤′00,c2 ++ZZ LLosβθ+ sinβ (1)
() ()
jj bj j
The following values are measured.
Z fly jib tip deflection
j
Z lattice boom tip deflection
b
Z lattice boom deflection at a distance L down from the boom tip
1 1
Z fly jib strut deflection at the tip
The following values are calculated.
6 © ISO 2014 – All rights reserved

Slope:
ZZ′=()−ZL/ (2)
b 11
Rotation:
θ= ZZ− L (3)
()
b 22
If slope (Z′) and rotation (θ) are not measured, the last two terms of Formula (1) may be deleted.
Figure 1 — Deflection measurement related terms —
Lattice boom with fly jib
6.3.2 Telescoping boom attachments
For telescoping boom attachment crane structures, no tip deflection limitations have been established.
Deflection of the mast attachment, the mast mounted boom, and fly jib shall be measured and recorded
when the system is stable.
8 © ISO 2014 – All rights reserved

6.3.3 Mast attachments
For mast attachment crane structures, no tip deflection limitations have been established. The deflection
of the telescopic boom attachment and fly jib shall be measured and recorded when the system is stable.
7 Facilities, apparatus, and material
7.1 A concrete or other firm supporting surface, sufficiently large to provide for unobstructed
accomplishment of the tests required. Where tests are to be performed on crawler tracks, the machine
shall be level within 0,25 % grade.
7.2 Means to measure levelness of the axis of the jib foot; accuracy 0,1 % of grade (see ISO 9373).
7.3 Means for determining the load radius to an accuracy of ±1 %, not to exceed 150 mm.
7.4 Means for producing traverse displacement of the suspended load and means for measuring the
magnitude of the displacing force; accuracy ±3 % of measured force.
7.5 Temperature compensated strain gauges, cement, waterproofing compounds, and other necessary
gauge installation equipment.
7.6 Strain recording system. It is the intent that commercially available, high quality, reliable instruments
be used in the performance of this test. Accuracy of the recording system shall be determined to be ±2 %
of the reading over the range of 500 μ m/m to 3 000 μ m/m strain (determined in suitable increments).
Calibration can be accomplished by electrical shunts or by pre-calibrated strain bar.
7.7 Test weights and lifting apparatus of known weights accurate to within ±1 %.
7.8 Means for measuring side deflection of the boom and fly jib within 50 mm.
8 Preparation for test
8.1 An analysis of each structure sufficient to locate highly stressed areas shall be made. The strain
gauge location and direction shall be determined from this analysis as well as from the use of other
experimental techniques where necessary.
8.2 Perform a detailed inspection of the crane to ensure that all mechanical adjustments and condition
of load supporting components conform to manufacturers’ published recommendations. Check that the
crane is equipped in compliance with the test specifications.
8.3 A previously un-worked crane should be given a “break-in” run at or near each anticipated test
loading to mechanically relieve residual stresses that might have developed during manufacture and to
minimize the possibility of “gauge zero shift” during the test.
8.4 Perform a thorough inspection after the “break-in” to reveal areas of high stress as evidenced by
paint checking, scale flaking, or other indications of deformation.
8.5 Bond strain gauges at the points determined by prior analysis (see 8.1) and any areas selected as a
result of the inspection conducted in 8.4. Only competent personnel using proven materials and practices
can be employed to ensure that all gauges are of the correct type, properly oriented, and securely bonded
to measure strains correctly.
8.6 Determine the minimum yield strength and the modulus of elasticity for the material at each
gauge location by referring to the material certifications, if available, applicable standards, or Annex B.
Determine the critical buckling stress when applicable (see Annex B).
9 Test procedure and records
9.1 Final test preparation
9.1.1 Locate the machine on the test course and lock travel brakes and latches. Level the machine to
within 0,25 % grade in the unloaded condition by shimming or by jacking. Do not re-level after the load
has been applied to the machine.
NOTE If the test is for operation on outriggers, jack the crane to a position where all the tires or tracks are
unloaded, unless the manufacturer’s rating chart requires some other conditions.
9.1.2 Connect strain measuring system and calibrate gauges and instruments. Correct any malfunctions.
9.2 Zero stress condition
If the assembled crane is to be used as the initial reference test condition, obtain these readings. If the
unassembled components are to be used as the initial reference test condition, obtain these readings.
Reassemble the crane and make all mechanical adjustments.
9.3 Dead load stress condition
9.3.1 Set the revolving upper structure to the specified position relative to the lower structure. Lock the
swing brake or latch.
9.3.2 Set the attachment angles and lengths to develop the specified load radius.
9.3.3 Read all strain gauges for dead load stress condition (see 3.6). Compute the dead load stress (S ) at
each gauge (see 3.7) and record on the test data sheet (see Annex D).
NOTE A new dead load stress condition is established each time the position, attitude, or configuration
is changed to suit the specified tests and operations: therefore, 9.3.1 to 9.3.3 shall be repeated for each new
condition.
9.4 Working load stress
9.4.1 Prepare a test load which together with the hook, block, slings, etc., weighs within ±1 % of the
specified load.
9.4.2 Suspend the test load (see 6.1) and apply side load (see 6.2) as required by specifications.
9.4.3 Read required strain gauges for working load stress condition. Compute the working load stresses
(S ) for each required gauge and record the test data. Measure and record tip side deflection due to
suspended load and side load.
9.4.4 Release side load and lower suspended load, returning crane to dead load condition. Read required
strain gauges and compare with reading taken under 9.3. If the deviation for any gauge exceeds ±0,03 S /E,
y
determine cause, correct, and repeat all procedures until consistent readings are obtained.
10 © ISO 2014 – All rights reserved

NOTE Since temperature changes and the loading from even a moderate wind on long booms and fly jibs
affects strain gauge readings, testing should be done under as favourable atmospheric conditions as possible.
Position the machine so wind loading does not reduce the stress induced by side loading.
Compute resultant stress (S ) per 3.10, for combined dead load and working load stresses and record.
r
Thoroughly examine the crane for any evidence which suggests a possibility of plastic deformation or
other damage having occurred during the test.
9.5 Overload test condition
9.5.1 Repeat 9.1.1, if applicable.
9.5.2 Position the crane (upper structure, boom) in the specified test position.
9.5.3 Set attachment angles and lengths to develop the specified load radius and record dead load
readings for Class IV gauges.
9.5.4 Prepare the test load (see 9.4.1).
9.5.5 Suspend the specified test load and adjust the boom angle(s; if necessary) to obtain the rated load
radius.
9.5.6 Observe the performance of the structure and note any evidence of possible failure.
9.5.7 Release the suspended load and return the crane to the dead load stress condition. Record the dead
load readings for Class IV gauges. (See 9.4.4)
At the completion of all applicable overload tests, the crane structures should be thoroughly examined
by eye using straight edges and other references, where appropriate, to determine any evidence of
buckling, permanent deformation, element out of line, etc. Scale flaking or paint checking can also be
indicative of stresses beyond the yield point. Disassemble the boom structure to the state necessary
to be ensured that all boom elements, extension cylinders, or elements, hoist mechanisms, suspension
systems, and other load-carrying elements can be inspected.
Record all pertinent data regarding the test equipment, crane being tested, results, and observations.
Suggested forms are presented in Annex D.
10 Stress evaluation
For purposes of this test method, stress is related to measured strain by the uniaxial stress equation
(see Formula 4):
SE= ⋅ε withinproportionallimits (4)
()
NOTE The simple uniaxial stress formula might not be sufficiently accurate for some areas of crane structures
under biaxial stress, and special consideration should be given in such cases (see Annex A).
Stresses in different parts of crane structures are evaluated for acceptability on the basis of criteria
appropriate to the area in question. These stress areas can be classed as follows (see Table 1 or 10.1
through 10.4 for minimum strength margins).
Table 1 — Minimum strength margins
a
Class III (column buckling area) Class IV
Class I (uni- Class II (stress
(local plate
form stress concentration
Curves Curves
buckling
Alternative
area) area)
A, B, C, D a, b, c
area)
Gauges must
b
X (erection n ≥ 1,3 and return to
n ≥ 1,3 n ≥ 1,0 n ≥ 1,4 n ≥ 1,2
1 2 3 3
c
loads) 2,2 ±0,03 S /E at
y
dead load.
Gauges must
a
n ≥ 1,5 and return to
Y (rated loads) n ≥ 1,5 n ≥ 1,1 n ≥ 1,6 n ≥ 1,3
1 2 3 3
b
2,5 ±0,03 S /E at
y
dead load.
Gauges must
Observation Observation Observation Observation Observation return to
Z (over loads)
only only only only only ±0,03 S /E at
y
dead load.
a
Refer to Annex B.
b
Critical buckling stress S is calculated by Jager’s equation.
cr
c
Critical buckling stress S is calculated by Euler’s equation.
cr
10.1 Class I — Uniform stress areas
Large areas of nearly uniform stress where exceeding the yield strength or yield point values will
produce permanent deformation of the member as a whole. Strength margin:
— n = S /S or S /S′ (refer to Annex A for S′);
1 y r y
— n ≥ 1,50 for rated loads;
— n ≥ 1,30 for erection loadings.
10.2 Class II — Stress concentration areas
Small areas of high stress surrounded by larger areas of considerably lower stress where exceeding
the yield strength or yield point values will not produce permanent deformation of the member as a
whole. Examples are points of rapid section change such as sharp corners, holes, or weld fillets. Strength
margins:
— n = S /S or S/S′ (refer to Annex A for S′);
2 y r y
— n ≥ 1,10 for rated loads;
— n ≥ 1,00 for erection loadings.
10.3 Class III — Column buckling stress areas
Areas in which failure can be considered to occur at some average stress value less than yield strength
or yield point. Examples are individual unsupported compression elements such as, but not limited to,
masts, struts, jib chords, or lattice, which require consideration as columns.
Strength margin (refer to Annex B).
If curves A, B, C, or D are chosen from Table 1:
— n ≥ 1,60 for rated loads;
— n ≥ 1,40 for erection loading.
12 © ISO 2014 – All rights reserved

For lattice structures, this criteria is intended to apply to lacing elements or chord elements between
lacing points.
It is not intended for evaluation of the overall latticed compression member.
10.4 Class IV — Local plate buckling areas
Plates, when subjected to direct compression, bending, and/or shear in their plane, can buckle locally
before the member as a whole becomes unstable. Local bucking is associated with wrinkling (initial
buckling), which permits the member to redistribute the loading to stiffer edges.
As loading is further increased, the stress in Class IV areas (see Figure 2) does not necessarily increase
in proportion to the load; however, considerable post buckling strength might remain. Requirements
are that Class IV gauges return to the dead load readings for all test conditions, including overload.
Class IV Areas (Typical 4 Sides)
Telescoping jib
Outrigger
box
and beam
Figure 2 — Local plate buckling areas
Annex A
(normative)
Strength of materials
A.1 Biaxial stress fields
In biaxial stress fields, there might be some error if the uniaxial stress given by S = E · ε (see Clause 10)
is compared to tensile yield point to determine the strength margin. The question arises when
consideration is given to the theory of failure applicable to the material being tested.
A.2 Brittle materials
The use of S = E ε (when ε is measured in the direction of maximum principal strain) presumes the
x x
applicability of the maximum strain theory of failure. This is the commonly accepted theory of failure
for brittle materials, and results given are valid for materials of this type.
A.3 Ductile materials
The distortion energy theory of failure generally is accepted as the performance criterion of ductile
materials subjected to biaxial stresses. This assumes that yield failure occurs when the distortion
energy under biaxial stress is equal to the distortion energy at yield stress in pure tension. An equivalent
uniaxial stress (S′) developing the same distortion energy as the actual biaxial stress is determined
for comparison to the yield point (S ) to establish the strength margin against failure. The equivalent
y
uniaxial stress is shown in Formula A.1:
′
S =−σσ σσ+ (A.1)
xx yy
Principal stresses are obtained from strain gauge readings by Formulae (A.2) and (A.3):
σ =+Evεε /1−v (A.2)
() ()
x xy
σ =+Evεε /1−v (A.3)
()
y xy ()
Principal strains are obtained by interpreting rosette gauge readings on Mohr’s circle or other convenient
means. Equivalent stress S’ can also be calculated from principal strains shown in Formula (A.4):
E ()1−−νε()εε++()νε ()εν+ ε
xy xy yx
S′= (A.4)
()1−ν
When three and four gauge rosettes are used (Figure A.1), the following equations can be used directly
to obtain the equivalent stress based on the readings of each of the legs.
Rectangular Rosette (Figure A.1):
14 © ISO 2014 – All rights reserved

c
b
c
b b c
a
a
a
Figure A.1 — Rectangular, delta, and T-delta rosettes
A.4 Ductile material approximate method
In most ductile material biaxial fields, the assumption that the equivalent uniaxial stress S′ equals E ε
x
will be accurate within 10 %. The main factors affecting the accuracy are
a) The ratio of minimum to maximum principal stress, σ /σ , and
y x
b) The ratio of shear yield to tensile yield, τ /σ
o o.
— σ = Tensile yield stress
o
— σ = Maximum principal stress
x
— σ = Minimum principal stress
y
Figure A.2 shows the magnitude of accuracy variance with respect to these two ratios, using Poisson’s
ratio ν = 0,285. The plot shows that as the condition approaches biaxial tension or compression error
can be 25 % to 30 %, as the condition approaches pure shear error can be 0 to 30 % depending on the
ratio τ /σ .
o o
The solid curve line in Figure A.2 is based on the distortion energy theory of failure as compared to
S = E ε . Distortion Energy Theory, while most generally correct, will check with the torsion yield test
x
(pure shear) only if τ /σ = 0,577. For materials in which τ /σ does not equal 0,577, the dashed curve
o o o o
lines (which do not correspond to any theory of failure, but only the tensile and torsion yield tests) give
some idea of the probable error. If a single gauge and S = E ε is to be applied instead of rosettes and more
x
complicated formulation, principal direction must be determined by some other means, such as paint
checking or (better) brittle lacquer.
1,1
y
ε
y
x σ
σ
1,0
τ /σ x
o o
ε
0,9
0,700
0,635
0,8
0,577
0,7
0,520
FAILURE IN SHEAR FAILURE IN TENSION OR COMPRESSION
PURE SHEAR PURE TENSION
0,6
-1,0 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1,0
PRINCIPAL STRESS RATIO σ /σ
y x
-1,0 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1,0
/
PRINCIPAL STRAIN RATIO
εy εx
Figure A.2 — Ratio of apparent stress to actual stress versus biaxial stress ratio
Recommended values to be used in calculating stress from measured strain are listed in Table A.1.
Table A.1 — Elastic properties of materials
Modulus ofe- Modulus of Poisson’s ratio
lasticity rigidity
a
(E) (G; Shear)
(Young’s; (10 Mpa)
10 Mpa)
Steel
Carbon and alloy structural 206,7 79,2 0,285
Cast 206,7 77,2 0,265
Stainless 137,8/192,9 0,305
Aluminium, structural 72,3 27,6 0,333
Magnesium, structural 44,8
Titanium, structural 89,6/110,2
a
The modulus of elasticity generally is quoted as a range; the figures listed are towards
the high and of the range for conservatism. The modulus of elasticity of some materials
varies widely with chemistry, heat treatment, or stress level. In such cases a range is listed,
and the proper value must be selected for the particular conditions in each case.
16 © ISO 2014 – All rights reserved
Єx
APPARENT STRESS S-E
Actual Stress S'
Annex B
(normative)
Column buckling stress
B.1 General comments
In deriving buckling curves or numerical tables for use in practical design, one has to be aware of some
inevitable imperfections of the member being considered, such as non-homogeneity of the material,
deviation from the assumed geometric form (initial crookedness), unintentional eccentricities of axial
load due to the unavoidable imperfection of shop and erection work. Each of these imperfections varies
over a wide range and combines with the others in each individual case in a particular manner. In order
to compensate all uncertainties encountered in practice, proper factors of safety or load factors should
be utilized.
Each compression member in a structure represents an individual case that must be designed according
to its particular loading and end restraint conditions.
B.2 Critical buckling curves related to residual stress
Various column buckling curves are shown in Figure B.2. Curves A, B, C, and D are the curves that are
related to residual stress and are used with the allowable stress method of calculation. A safety factor
must be applied to the critical buckling strength obtained from Figure B.2. Table B.1 lists the Yield
Strength, S , the Proportional Limit, S , and the Residual Stress, S for each of the four material types
y p RC
(A, B, C, and D).
The shape of these curves can be defined by three parameters: the modulus of elasticity E, the proportional
limit S and the material yield strength S . Axially loaded members can buckle elastically or inelastically,
p y
depending on the stress levels. At stress levels below the proportional limit S , axially loaded members
p
buckle elastically. Inelastic buckling of the axially loaded members occurs at stress levels above the
proportional limit S . For inelastic buckling, relative buckling stress (ratio of buckling stress to yield
p
strength) is a function of the ratio of residual stress to yield strength as shown in Formula (B.5).
The residual stress is included directly in the buckling formulae. No factor of the uncertainties such
as out-of-straightness. is incorporated in the formulae. The buckling curves are indeed for “specially
straightened material”. Nevertheless, a strength margin of 1,6 (see Table 1) must be applied to the
critical buckling curves. This strength margin overcomes such uncertainties that would affect the
buckling strength of the members.
Applicable formulae for the elastic buckling of columns (S  ≤ S ):
cr p
π E
S = (B.1)
cr
(/KL r)
or
X = (B.2)
λ
Applicable formulae for the inelastic buckling of columns (S  ≥ S ):
cr p
SS()−S
py p
SS=− (/KL r) (B.3)
cr y
π E
SS=−S (B.4)
py RC
or
S S
RC RC 2
X =−11()− λ (B.5)
S S
y y
As shown in Table C.1, a value of S = 103 Mpa can be assumed in lieu of specific residual stress
RC
information on the following steel materials:
a) hot finished shapes in the as-rolled condition;
b) quenched and tempered shapes with stress relief heat treatment;
c) cold-drawn shapes with stress relief heat treatment;
d) fabricated welded shapes with stress relief heat treatment.
On other materials, a value of S = 0,5 × S can be assumed in lieu of specific residual stress information.
RC y
Table B.1 — Residual stress assumption
S S
y p
Residual stress assump- Yield stress Proportional
a
Curve
tion (Mpa) lLimit
(Mpa)
S = 103 Mpa A 690 586
RC
(lowresidualstress)
B 483 379
C 345 241
D 248 145
S = 0,5 S D 690 345
RC y
(highresidualstress)
D 483 241
D 345 172
D 248 124
a
Refer to Figure B.2, Critical buckling curves. Steels other than those listed can be used,
provided it can be shown they are suitable for the application intended.
The following values can be used for the end restraint factor K.
a) For chord members, K = 1,00.
b) For lacing members with full section connection to tubular chords, K = 0,75.
c) For lacing members with full section connection to angle or tee chords, K = 0,90.
d) For lacing members with reduced section connec
...