Ferro-cement for ship hull construction - An alternative solution of the strength calculation quandary

By sly. ¡ng. Jane K. Johansen

confusion into the discussion of ferro-cement properties. It is important to point out that reinforced concrete and ferro-cement are two quite different materials, not primarily with an eye to the weight, strength and panel thicknesses in a practical design, but more due to the fact that ferro-cernent properties are quite different from those of ordinary reinforced concrete.

People accustomed to hulls made of wood, aluminium, glass-reinforced polyester or steel, will perhaps hesitate when hearing about planing boats made of ferro-cement, and boat enthusiasts will undouptly have the old heavy reinforced concrete cargo

ships in mind. However, there has by now been built several fast planing ferro-cement patrol boats for military service.

The tendency to think of the inferiour elastic properties and low impact strength of ordinary reinforced concrete when hearing about thinwalled ferro-cement constructions could be one of the main reasons for the slow development of ferro-cement as a boat

building material. As early as before the second world war Prof. Pier Luigi Nervi carried through hi well-known

investiga-tions on ferro-cement.

Most ferro-cement boats built until now hive been constructed by hobby builders as one off hulls. The building methods were invented by such builders, and were not suited for a rational

series production. When using these traditional building methods

for single ferro-cement hulls, built in developed countries, the

labor costs will be about 5 times the material costs, and even if the material cost is kept low, the total building costs of the hull will be nearly the sanie as for hulis made of steel or timber. The future of ferro-cement boatbuilding will therefore depend on the possibilities to develop new and ratiorial construction

methods. UK builders and builders in New-Zealand and in USSR

have perhaps pointed out the right way to go. It seems clear

that the building methods used by hobby builders should be

replaced b)- an advanced use of prefabricated hull sections and by the use of jigs in production. A suitable production technology will give low labor costs and low total hull costs in series

pro-duction.

The development of advanced production methods should be lollowed by arm evaluation of the strength calculation methods in order to produce economic designs and low hull weights.

When it cornes to the question of strength calculation methods

in designing, it seems that some controversial aspects have appeared.

The properties cf ferro-cernent

b

Schiff und Hafen, Heft 4/1973, 25. Jahrgang 327 t

10JAN. 1974

ARCHIEF

COVL,t-L4

FerroCement

fr Shp uH Corstructon

an alternativè soIuton of the

strenght cacuiation

quandary?

Introduction

The slow development of ferro-cement in ship arid boat building seems strange considering the fact that the properties and

possibilities of this material were dicovered before the second

wor1d var.

The unsuccessful development of big and heavy concrete ships built between the first and the second world war could he one explanatiòn. At that time the lack of construction steel gave rise to the reinforced concrete ships, hut the big deadweighf-displace-ment ratio of such ships was a drawback seen from an economic point of view. 'Later. there has undoubtedly been brought some

- C. E

rrRRo-Cq(Nr RErNçoRc"o CO4'CE7

Fig. lA Fig. lB

The typical relationship between stress and relative elongation fbr ferro-cement under axial load is shown in fig.

IA, :ht o

ordinary rèinforced concrete under axial load is sketched in fig. IB. Looking first at the stress-elongation diagram of ferro-cemerit, one finds that within the sector 0<e<r0 the deformation of the ferro-cement material is elastic, but there is no linear relatiom-ship

between stress and elongation.

The interval e>e is called the crack formation sector of the

ferro-cement material. When going from the - sector of e!ìstic

deformation into the sector of crack formation, no sudden diaries can be observed, and the smooth curvature of the stressreiormga-tion curve will continue far into the sector of crack formastressreiormga-tion. The "yield point" of the material (e = co = 10-25 .

r-3) ja

the point where the microcracking begins. \Vhen o increases, the

microcracking will incr5ase, and it will gradually become a

macrocracking followed by visible cracks. The number of and :he size of the cracks will increase until the breakdown condition is

reach ed.

The stress-elongation diagram of ordinar)- reinforced concrete will be quite similar to that of ferro-cement at very small values of . The diagram of fig. lB could be that of a concrete under axial load, reinforced with a few iron rods. At a esrz:in relative elongation parts of the reinforced concrete cross section under consideration have reached the stage where the actual

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Technische Hogsch--c.1.

-

Deift

Ferro-cenient mainly consists of cement, sand and dispersed

reinforcing steel. Compared - with ordinary reinforced concre:e.

it behaves mors like a homogenous material when it is loacd. The dispersed start of steel reinforeehient in ferro-cement ?°-vides a muds higher specific adhesion surface related to

volume of material - than in ordinary reinforced concrete.

When an unreinforced concrete beam is loaded axially by a force F, this force will approximately be distributed as an ever. normal stress over the cross section area of the beam. .nd if

the normal str.iss is rioted by cm, the normal force acting on a

small area dA of this section could he expressed by dF = cm dA. The breakdown condition will be readied when o equais the

ultimate stress of the concrcte

At the cross section -of a similar loaded ferro-cerrient be some p.srt of the force F will be distributed as normal stresees

over - the cross section area, but another part will be

:r.urs-ferred to the adhesion surface of the steel fibers dispersed at ny

direction or angle through the section area under consideration. Noting the adhesion force per unit adhesion surface by r and

the total effective adhesion surface at the small section area dA h) dA3d, the force balance of this small ferro-cement etusa section area could be expressed by the equation:

dF = . dA ± r. dAmid.

For the entire cross section the force balance will then be:

- F

ferdA

+ f

rdAa

A

This leads to the conclusion that the material strength increases with the adhesion surface. i.e. the strength will increase with the degree of dispersion of steel reinforcement.

:.D:-mi Stresses equ.il the :ensilc stress of unreiriforced concrcte. zd sorne crckjng xviI _{ke pIac ..At this sge the concrete s} no: able to bear any !od. _{nd the entire lo.si must tlszcfore}

h _{csrrid by chc stcel rnforccmenc cross section arca of th} section, _{i. e. the cross section area of the steel rods. This change}

cn be observed as a break-point of the stress-elongarioi

dia-grrri, at e = C) US fig. lB. I the Sector where che entire load i5 carried only by the steel reinforcement (.t>e), the diagram is nearly rectilinear as long as the elastic limit of the steel is not exceeded (up to the yield point of steel).

3efore entering a short discussion of existing _strength calcula-tioc _{methods. some important considerations should be stared} as _{follows: Neglecting the creep effect of reinforced concrete}

Loder a Static load, _{reinforced concrete constrtctions with no} special demands on fatigue strength and _{wacertightness can be} !oaded far into the cracked sector of the stress-elongation diagram, pig. _{IB (>5ç). Concrete constructions on land cari also}

be diniensioned for a working _{stress in chis sector, and one will at}

de same time be able

to retain the necessary safety against

areakdown. It should be mentioned that both the classical strength :alculation methods and those of newer origin for approximate

trength estimations of reinforced concrete constructions are based )n certain assumptions:

1. _{The strength of reinforced concrete is given by the bearing} capacity of the steel reinforcement, i.e. _{the reinforcenserjt} factor u - FJF 100 (0/o) is the main characteristic factor of strength.

= cross section area of the steel reinforcement in the reinforced concrete cross section.

F = entire cross section area.

2 _{For practical strength estimation the functioning of the} concrete in the elongated zone is not taken into account.

Ferro-cement constructions loaded with _{a constant static load,} ithout any requirements _{to fatigue strength, can be designed} a working stress in the macrocradç sector of the stress-elonga-on diagram.

Ferro-cement constructions especially designed for alternating

)ads (offshore constructions) should be _{dimensioned for maximum} ads giving stresses not higher than _{the stress at the stage of} ginning micro-crack formation. In other words, the alternating orking stresses should not exceed _{the "yield stress" of the}

aterial. T'ne strength _{calculation theory of ferÑ-cenient for}

fshore designs undergoing alternating loads, should consider the eSfic strength characteristics of ferro-cement:

The strength of ferro-cemerit is _{primarily given by the} surface area of steel per unit volume _{of material, i.e. the}

adhesion _{surface per unit volume: K ir cm2/cm3 (the}

adhesion surface coefficient).

The reinforcement factor u is only of secondary im-porrance as far as strength is concerned.

The ferro-cement material should be considerèd as a homo-genous material.

The position of the neutral axis for _{cross sections of beams} and plates under load will shift according to the magnitude

of th present load, i.e. the modulus of elasticity:

E .4_ _{will be different for elongation and compression,}

d

and it will vary with the load.

Seen from a practical viewpoint, the _{strength calculation}

should be as exact as possible _{in order to produce}

economic designs and designs of as low weight as possible. The calculation _{theory should at the s.ìine time be}

as simple as _{possible in order that the designer may derive} scantlings by slide rule methods. The calculation theory

should possibly permit analytic solutions of the strength problems, without a complicated use of computer techniques and without the need of enlarged _{preparations of computer} data inputs.

For years, various series of cernent hive beers carried out North-America and in USSR. portant reports by (1), (4), (5)

laboratory investigations on ferro-st technical universities, moferro-stls' in rn connection with this, the ins-and (6) should be noted.

When it comes to thc---question of strength calculation of ferro-cernent, it looks as if all practical estimations up to now have been based mainly on classical strength calculation methods for ordinary reinforced concrete, or on finite element analysis, as for example described by (7). Finite element analysis solutions are often accompanied by ars enlarged use of _{computer techniques.} The existing classical methods _{are either based on the simple} linear theory of structural mechanics, i.e. a constant Young's Mo. dulus E is assumed for the ferro-cenient _{material, or else based}

on the stage of breakdown condition for the section under

consideration. 1f the breakdown condition or critical state in respect to bearing capacity is used for calculating the working stresses, the stress distribution is taken constant over the

compressed zone and over the elongated zone of the section. The working stresses are theis calculated, based _{on the constant stress} distribution corresponding to the breakdown conditions.

When using classical methods in ferro-cement _{calcularibns, it} seems that scantlings get stronger and heavier than _{necessary, and} one should have in mind that the classical methods _{are developed} especially for ordinary reinforced concrete having the reinforce -ment factor u as its main strength characteristic in the _{range of}

permissible working stresses. As mentioned before, the main characteristics strength factor of ferro-cement is the specific

adhesion surface coefficient K-T.

Lastly, the alternative theory developed by (1) should be

mentioned _{(modified method of structural mechanics). In this}

very interesting theory the fcrro-cement material is _{assumed to} be homogenous and isotropic, and two different constant values of the Young's Modulus _{are used, one in the elongated zone of} the section under consideration, the other in the compressed zone

of the section.

-Nonlinear strength calculation theory forferro-cement constructions

Any nonlinear relationship will complicate the _strength calcul-a-tion method, and iteracalcul-a-tions will often be _{necessary when solving} the equations of normal force and moment balance. The iteration calculation work can however be kept to a minimum provided that the main p-art of the calculations can be done by means of a pure analytic method, and provided that _{some simplifications} can be allowed.

In the strength calculation method proposed by (2) mie has tried to incorporate and take care of the nonlinear relationship between stress and relative elongation. _{At the same time it has} been vçry important to derive a _{sinsple calculation method in}

order to limit the amount of calculation _{work. The calculation} theory is _{based on the hvpothss that plane sections of a beam} undergoing bending remains plane after _{deformation. Since,} how-ever ferro-cernerit is _{an inhornogenous material, the assumption} of a linear relative elongation (conspression) distribution over the cross section of ferro-cen:cnt beams in bending is not quite

correct. It is assumed that this lack of accordance with the

un-known elongation (compression) _{distribution over the cross section}

will be of only marginal significance with respect to stresses. This should perhaps be verified _{by series of sample tests. Further,}

the strength calculation theory proposed by (2) is arranged so as to obtain a direct incorporation of the strength _{properties of the} ferro-cement material under consideration. In addition this theory takes into consideration the fact that for a given material, the

stress-elongation diagramm of .sxial expansion_{will be quite different}

from that of axial compressiòn.

In fig. 2 and fig. 3 (taken from (I)) results are shown from

sample tests _{of ferro-cernent specimens. Diagrams of the type} shown in figé 2 (axial expansion) are those of most interest in connection with the _{calculatioti method proposed by (2), but} similar diagrams of axial compression will be needed. Therefore, the sample testing should be planned in order to get diagrams

b

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l-e/o/h,e e/o,'oMo,, E/a5 o

1q1,qL ExPmysrcw FIg. 2 Fig. 3

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.-..e 2 (/o-... I... O). '-,ox xxiv)

v... ,.r.A e,..Ñ.,.,.., _,...ì>.

of the type indicated by fig. 4. In addition it may be necessary to fulfil compression tests with pure unreinforccd concrete bIods in _{order to examine the quality of the mortar mix and the} curing process.

The nonlinear calculation method of (2) is based on a stress function for the nominal bending or axial stress:

co _{f (e, a, fi, r, 2, E0) (1)}

e = relative elongation/compression.

a and fi are coefficients lationship or elongation consideration.

r and ;. are coefficients lationship or compression

do

E0 = - when e=O.

de

The above coefficients must be obtained from sample test

analysis.

The stress function f will result in complicated strength calcula-tions. \Vithout any simplification, computer work will always be needed. \Vjth a suitable adjustment of the conditions for determi-nation of coefficients a, _fi, r, and . however, a simplification of the above stress function may be allowable in order to decrease the calculation work. This adjustment will give a modified and more practical stress function:

= g (e,a,_fi,a', 2) ₍₂₎

Formulas for the maximum stresses and the stress distribution over the cross section area of beams can then be established by indicating the stress-elongation

re-properties of the material under

indicating the stress-compression re-properties of the material.

k

e::l co0..Er.iR ,._E._

1pJuIP

I I 14

LL

'V cc d y dx rel' e/i'0¿'D

ttOx"

e p C0M11(ß TWO. War R00 A/IO P/IRE MEEN R110ttOaC (N (NT

inserting the equation (2) in the equations of axial force balance and moment balance:

N fb . cody O (normal force)

h ₍₃₎

M f b . o- y dy = external moment

h (4)

h entire height of section

y' = distance from neutral axis of the section to the fibers

under consideration.

b b (y) breadth of section at the fibers under

considera-tion.

The determination of shear stress distribution over the cross section area is niore complex. As mentioned earlier, the position of the neutral axis of the cross section will shift with decreasing or increasing load. The shear stt:ess t must therefore be determined by a function:

5.

(5-= F (5, i, fi, V, 2,

(

(

x = coordinate along the beam ax

y = height from neutral axis to the fiber under consideration

Schiff und Hafen, Heft 4/1973, 25. Jahrgang 329 (5) 5.'"R 1 (f'r'.n (i),:a'..,pFe )(Exj 70

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Fig. 4 V Fig. 5 lxv, fl..p1. le-514. CCOO...,.. » \:'-.., - -'-y -'-1 ..,.,

rOp.ej ¡'007 ,J,,,$ ¡'f . .''.' 'o'er S200 Fig. EA 3.2

(t3jA])

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Fig.6B SrCr'.r., Xi'ZT (;_ (1) 10 0 8-r 9 -_ prrIJeS )Ç,. 2.02 o; = e o

Schiff und Hafen, Heft 4/1973, 25. Jahrgang

\Vhen using the modified funcron of equation (2), a simple iteration calculation is needed for the estimation of normal bend-ing stresses. This iteration may at the same time. give the necessary

values of

kor 2.S2

i ofl.

O

y Il

f dv\

j and

_{I r- I}

for the calculation of shear stress

' Sx F

\dx/

distribution over the cross section.

As stated earlier, the strength properties of ferro-cemenc will depend mainly on the specific adhesion -surface coefficient K..,.

c:s- The most common types of ferro-cement used in boat building

are reinforced -as follows:

Wire mesh steel reinforcement only.

Combined one-way rod and wire mesh steel reinforcement. Combined two-way rod and wire mesh steel reinforcement. For practical dimensioning, using one forni of meshes, the value of K., _{is determined with a formula proposed by (1):} O-' 5S.t.

Fig. 6C:-Dlagran, a: Nominal bending stress at section I, calculated by the method cl (2), nonlinear theory. Diagrams b and C: Nominal bending stress at section I, calculated by the method01(1).

9.5'000 )ç.o/,_° Erjt0j1,0 kpJr_° Fig. 60: DIagram d: Shear stress at section II, calculated by the method

of (2), nortllner theori.

Diagram e: Shear stress at section Ii, calculated by the methòd of (1)

4.'...e 0/.lr.4.

(

= variaion in clic o-I-ratio along the beans axis.

variation in the neutral xs position along the

dx / _{beam axii}

-:0., d = wire diameter of the meshes (cm).

-a size of screen meshes (cm).

n = number of screen layers in a section.

- h = height of section (Cm). -

-If _{the ferro-cement designs are to be of the combined}

rein-forcement types (2. or 3.), corrections in K estimated by equa-tiOn (6) _{must be done due to the presence of iron rods in the}

section area.

Before entering a strength calculation of a ferro-cement

construc-tion, the values of _{a, fi,} i' and , must be known. Having

determined the value of - K., by means of formula (6), with or without corrections, for the present new design the

correspond-ing values of es, _fi, i- and ¿ should be taken from diagrams of the

3 types shown in fig. 5. _{These diagrams should be based on data}

obtained by enlarged laboratory tests of ferro-censent samples of different types and .'ith varying values of K..,.

Sample strength calculations

-Some elementary problems will be shown here in order to indicate

results obtainable by means of the nonlinear strength calculation theory.

The point-loaded ferro-cement beans of fig. 6A, with a rectangular

cross section and a reinforcement Structure of the wire mesh type - shown in fig. 65, was strength calculated and the results compared with those obtained by using the modified method of structural mechanics evaluated by (1).

It should be mentioned that if some simplifications_{are assumed.} the theory of (1) can naturally be developed from the _nonlinear theory. The nominal bending stresses at the beam midpoint section (section I), arc seen in fig. 6C. The bending morflent corresponding to the stress figures -shown is 5cc- kpcm. When using nonlinear theory (Curve a. of Fig. 6C) _{the position of the neutral axis will be}

given by the magnitude of the load. The neutral axis will move from the C.G.-axis of the cross Section when the load increases: As can be sects, _{the curves b and c of fig.}6C are the nominal bending stresses of secion I, calculated by the method of (I). As mentioned before, in _{this theory constant values for the Young's} - Modulus must be chosen, E2 for the, elongated zone and E _{for the} - compression zone of the section, - and if a certain ratio Ec/Ee is stated, the position of the neutral axis will be fixed, independent of the magnitude of load. The drawbadç of this theory is the fact

0r.. '.4-', .j.

k

o; s'a. b. o; = os'. p C. Ê. ÇS000 Op/o... E .14'2 SOU Ç500o r 100020 2 S.ree, C'/Oo/,.,'ea'

r.I s#,.essez al óea T Croo.,-. ser,o,..

e "o#hrd o! -(2),

"O',i,',ea.-Slrc..e O,,/. a-;.e -'er.', ,

o.,

c- 2 , i, o 3.5' g e

al' 2CC/br, 8p'cI;o 'eo /'lrr 5000 irpro..

F1'j.7

K.0 = 5.65.

--

n h

that the calculated maximum stresses of the section are higher than the actual ones. The chosen value of the Youngs Modulus is only a mean value for the relationship between relative elongation and stress, and it is always difficult tO assume a mean modulus of elasticity which is representative for the actually stress and load

condition.

The shear stress distribution over the cross section II of fig. 6A is shown in fig. 6D. The two shear stress figures, diagram d cal-culated by the method of (2) and diapanm e calcal-culated by the method of (1) are nearly similar to each other.

The diagram of fig. 7 shows thè nominal bending stresses estimated

by the method of (2) for a T-section carrying a load of M 6000 kpcm. The "yield point" of the ferro-cement type used in this beam is about a = 15 10, i.e. the yield stress is o 33 kp/cm2 (K = 2.52 cm/cm8). As seen from fig. 7 the present maximum stress of the elongated zone is a = 46 kp/cm2. The maximum allowable alternating elongation stress of this beam used in an offshore con-struction should not exceed the yield stress n.s = 33 kp/crn, but if

this beam is used in constructions on land, carrying only statical loads, a working stress of o. = 46 kpfcmS should be allowed.

The overall nominal bending stresses were calculated for the mid-shipsectioñ of the diesel yacht shown in fig. 8. The ferro-cement structure of the bottom and side plating is of the combined type

shown irs fig. 8, with a skin thickness of 21 mm or cä 7/8". The midshipsecion, shown in fig. 9, was strength calculated for a bend-ing moment of 40 tm (tonnmeter) and for a bendbend-ing moment of 120 tm. The nonlinear calculation method was used and the stress diagrams in sagging arc seen in fig. 9. Since the yield stress of the ferra-cernent type shown in fig. S (total K. = 1.79 cm5icm3) is about 36 kp/cm5 for elongation, a maximum midship moment of 40 tm in sagging could be allowed for this 45' vessel, but a midship moment of 120 trn would be a too high load. However, the

expected -maximum midship moment in service for this displacement

vessel of 45' length will hardly reach the value of 40 tm, a figure

of 20-25 rm would be of- better relevance.

F=' , "rJ. 5a (3p ;_... _

f.

C'). '-p.' - --- ----.._____L

_0"--.

7...,'. ..d ., ¿,..3', s.,_ .i .;,_.,s.

2.sr'-_'

7..j fr - - p.0.3CC ,a. a5s. A Fig. 8 1 Fig. 9

Therefore a skin thickness of "-%" would perhaps uit the overall strength requirements, provided that the value of the cor-rected toral K., remains 1.79 cm2/cm3 or exceed this value. Alter-natively a ferra-cernent structure of the combihed one-way rod and wire mesh type could then be used. Finally the size, spacing and arrangement of ferro-cement frames and floors will naturally

in-fluence the skin thickness requirements. Bibliography

(1( V. F. Bezukladov; K. K. Arnel'yanovith. V.' D. Verbitskiy, L. P. B3gcyav-ertskiy: Korpusa sudO', ir arnotserneñta. (Ship hulls made of reinforced concrete). Shipbuilding Publishing I-louse, Leningrad. 1968

121 J. K. Johansen: Strength calculation of ferro-cement for ship hull con-.

structiort, based on the assumption that the material is homogencus and isotropic. Report to be published December 1972.

Prof. Dr. E. Mârsth: Der Eisenbetonbau. Seine Theorie und Anwendung. Stuttgart 1912. Verlag von Konrad Witiwer.

Charles Darwin Csnby: Ferro.cernent with Particular Reterence to Mtrine Applications. SHAME-report 1969.

J. F. Collins and J. S. Claman: Ferro-cenient for marine application. An engineering evaluation. SHAME-report 1969.

H. F. MCihlert: Analysis of ferro-cernent in bendin. SHAME-report1969.

Jan C.Jotriet and Gregory M. McNeice: Finite element analysis of rein-forced concrete slabs. Journal of structural division. Proceedings Ci the American Scoiety of Civil Engineers. March 1971.

Schiff und Hafen, Heft 4/1973, 25. Jahrgang 331

sl,essts ,d a a

a55;j