1539

STRUCTURAL DESIGN DF REINFORCED MASONRY LINTELS

OR. ARMIN OHLER German Masonry Association

Schaumburg-Lippe-Str . 4, 5300 Bonn 1, West Germany

ABSTRACT

lhe paper outlines the practical design of reinforced masonry lintels in bending and shear. Oesign charts are developed which enable the desig­ner to easily determine the dimensions of the lintel as well as the amount of rebars required for a given span and loading . lhe structural detailing is explained, and examples are given demonstrating the design of reinforced masonry lintels.

INTROOUCTION

In Germany, as well as in many other countries, among architects and struc­tural engineers the use of reinforced masonry lintels as structural ele­ments in loadbearing walls is not common practice. lhough being widely used in facade walls loadbearing beams supporting roofs, floors or gable walls tend to be designed in reinforced concrete or steel. However, mixed structures, i . e. concrete or steel members as part of a masonry wall, are characterised by considerable disadvantages in terms of the thermal conductivity of the wall. The good insulation provided by the masonry is undermined by zones of high thermal conductivity of other structural materials; in consequence, additional insulating measures causing costs are required.

Although masonry is regarded to be weak in tension it may well be used in members subjected to bending if, with analogy to reinforced con­crete structures, the tension forces are taken by the steel reinforcement.

In the following the structural design of reinforced masonry lintels in bending and shear is outlined. The design is based on the Building Guide line 111 which, in the absence of appropriate rules in the current German masonry code of practice, gives guidance on the design and construc­tion of reinforced masonry beams.

DEFINITION

Reinforced masonry lintels complying with 111 are lintels with limited dimensions in height and length. lhey are mainly used in normal houses, dewellings, and low rise industrial buildings. lhey are characterised by a U-shaped tension flange carrying the reinforcing steel. For good corrosion protection the steel rods are embedded in concrete. lhe masonry is traditionally exected on top of the flange featuring horizontal bed joints and vertical partly or completely filled mortar joints. Fig . 1 shows a typical example of a reinforced masonry lintel. lhe material of the U-shaped unit corresponds to that of the masonry forming the com­pression zone and may be clay, calcium silicate, light-weight concrete

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layer

I.. li=I-2~ .1 I;A~115cm I s 3.0m

Figure 1. Side view of a reinforced masonry lintel

pumice) or aerated concrete. In case of light-weight concrete the tension lange may also consist of precast bulk concrete elements. In case of lay bricks soldier units may be used with rebars passing through the erforations and holes of the bricks (fig. 2).

---..lI 11 11 II 1/ IL ~DDDDDDCJDDCJC::= ~I 11 II 11 IC~[

::Jn 000[]] QLJ D[

[ reinforcement

I

Figure 2. Lintel with soldier clay bricks

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According to / 1/ reinforced masonry 1inte1s sha11 meet the fo11o­wing requirements:

tension flange: - minimum width of 115 mm - minimum height of 60 mm - type BSt 400 S or BSt 500 S exc1usive1y

concrete infi11 of the UZshaped unit having a minimum averaêe compres­sive strength of 30 N/ mm (concrete c1ass B 25) and 29 N/ mm (light-­weight concrete c1ass LB 25), respective1y .

- minimum concrete cover of 20 mm

compression zone: 2 - minimum average compressiv2 strength of units 15 N/ mm (unit strength

c1ass 12), and of 2,5 N/mm (mortar c1ass MG 11) foZ mortar - design compressive strengh of masonry BR = 2,5 N/ mm . - maximum effective height taken for the structura1 design 1/ 2,4 (1 = 1in-

te1 span, cf. fig o 1) - a1though undesirab1e it may be necessary to use concrete for constructing

the compression zone, e.g. if the structura1 design requires a very low height of the 1inte1. In this case guide1ine /1/ refers to the de­sign of concrete structures. Detai1s on this may be obtained from /2/ and /3 / .

FLEXURAL DESIGN

In princip1e, the design of reinforced masonry 1inte1s is carried out in ana10gy to reinforced concrete structures. However, both different u1timate strains and a11owab1e design compressive strengths have to be taken into account. According to test resu1ts obtained by / 5, 6/ an u1ti­mate strain of E = 3,5%0 is adopted being conservative for a11 common types of masonry~WFig . 3 shows the stress-strain-re1ationship used as a basis of the designo Assuming a cracked tension zone for the masonry subjected to bending the compressive force taken by the masonry compression zone at u1timate is expressed by (cf. figo 4)

x

Dmwu S bomw(y)dy = bXC{RBR (1 ) being o

é (2 ) ~ = ~ (6 -é )

12 mw

b width of linte1 BR design compressive strength of masonry

As is th '2 case for concrete /4/ eqn . (2) expresses the coefficient Oi- as a function ~" the strain at the upper side of the 1inte1 t descri­b~ng th2 parabo1ic shape of the compression area An0 The distancWwx of the neutra1 axis from the upper side of the beam mày be expressed as a function of the strains of the masonry and the stee1:

x . h (3) E +E mw s

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O'mw

fi R

( Emw2) (}'mw=fiR cmw - -4-

-2%0 1Emwl

Figure 3. Stress-strain relationship of masonry

LH ___ k Emwu r ... O"'mwu ~ f3 R

J -o

Dmwu )

As O"'su Zs

Mu l Z =kz·h

-Figure 4. Stress / strain distribution; inner forces of cross section

In order to determine the inner lever arm

z k· h h - a z (4)

the distance a, too, may be expressed as a function of the strains (cf. i 4i for concrete)

a 8 - Emw

k a . x 4 (6 - é mw)

From eqns. (4), (5) and (3)

k z 1 _ ! = 1 _ ka • x

h h 1 - ka kx f (Emw ' E. s )

(5 )

(6 )

is obtained, which means that also the inner lever arm z is a function ofe and ES' respeç~l~ely. This leads to the inner moment mw

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M O z u mw,u (7)

and, wit ~ t he inserti on of eqns. ( 1) , ( 3) , (4 )

M u bh 2B R Rkxk z =~. M (8)

with M = acting moment t = safety factor 1,75

Fr om eqn. (8)

(9)

is obtained which den otes the degree of exp10itation of the section as a function of the strains of masonry é and stee 1 ES' 111 prescr ibes that max E = 5%0 and due to fi g . 3 ma~wE = 2%0. EConomi ca 1 use of a gi ven 1 i nt~l sect i on i s made for é léS-vWfues as 1 i sted in tab 1 e 1. mw

TABLE 1

Design coefficients for reinforced masonry 1inte1s

~R = 2,5 1.IN / m2

ESt 420 S BS t 500 S - E: mw / E: s

kh

k k k k e,o I 'c o] s s x z

29, 74 4, 25 3,57 0,06 0,98 0, 3 1 5,0

18 . ó2 4,30 3, 61 0, 09 0,97 0,5 I 5, 0

13,87 4,35 3, 65 0,12 0, 96 0, 7 I 5, 0

i 1 , 26 4,40 3, 70 0,15 0,9 5 0, 9 I 5,0

9, 61 4, 45 3, 74 0,1 8 0, 94 1,1 I 5,0

8 ,48 4, 50 3,78 0, 21 0, 93 1,3 I 5,0

7, 67 4, 55 3,82 0, 23 0,92 1,5 / 5, 0

7. 07 4, 59 3,86 0,25 0, 91 1, 7 I 5, 0

6, 42 4,67 3,9 2 0,29 0,89 2,0 I 5,0

6,2 1 4,71 3, 96 0,31 0, 89 2,0 I 4,5

6,00 4,7 6 4,00 0 , 33 0, 88 2,0 I 4,0

5. 78 4, 82 4,05 0 , 36 0, 86 2,0 I 3,5

5. 56 4, 90 4,12 0 , 40 0, 85 2,0 I 3,0

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The size of the rebar needed is determined by

M u _ toM _ Z -----A B ( 10) s k oh s s z z

yielding As ~ !:! = k M ( 11 ) s B ok h h s z

For a given cross section of a beam and the acting bending moment M the kh-coefficient is calculated with eqn. (9), and then the k -coeffi­cient is obtained from table 1. If there is an additional normalsforce N M is replaced by

MS d M - N (h - - ) 2

( 12)

SHEAR DESIGN

The shear failure mode of masonry lintels differs substantially from that of concrete lintels. As illustrated in figo 5 load transfer to the support is achieved by an inclined compressive force producing shear failure in the bed joint. The shear resistance required is dependent on the inclina­tion of the compression force D; as a measure for this the shear ratio

À max bendíng moment M max shear force o effectlve helaht ~

(13 )

may be taken. As qualitatively illustrated in figo 6 the shear resistance decreases with increas in g À. If À falls below 0,6 failure is governed by the vertical compressive strength of the masonry rather than the shear strength of the unit/mortar bo nd.

p p

tendon

i Imox M/z I z

.r - I : mox MIz I I

mox Q

L~:}·mQXO O H =mox a· z

Fi gure 5. I nterp 1 ay of force s in 1 i nte 1 and support

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In order to determine the allowable shear resistance of a masonry lintel, the guideline / 1/ gives the formula

with 't'uJ 6,11 À

r-- À+O,4 lulQ=L ·b·h--lul À-O,4

allowable shear st rength = 0,1 N/ mm 2

width, effective height of lintel shear ratio according to eqn. (13)

( 14 )

In practice live load on the lintel in most cases will be uniformly distributed and the statical system will be simply spanned. Hence, eqn . ( 13) becomes

and eqn. (14)

lU 1 q

4 h "

h' h+ 1,6--1 2Z ·b --­lul 1-1,6h

being lul q = allowable uniformly d{stributed load on lintel 1 = lintel span

( 1::.)

( 16)

As shown in fig , 6 À shall not fall below 0,6 to avoid compression failure of the masonry. Therefore, guideline / 1/ limits the maximum effec­tive height to

Q) u

~ c:

'" '" Q)-I-' .c:'" "' ....

'" Q) ~

max h

0,5

1

2,4

compression failure of masonry

failure of unit/mortar bond

-shear ratio À

Figure 6, Ultimate shear force versus shear ratio

( 171

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The insertion of eqn . (17) in eqn. (16) 1eads to an upper 1imit of lu1 q

grenzq 4,161: 'b zul

which, together with the a11owab1e 10ad lu1 q is eva1uated in figo /7/ for the 1inte1 width of b = 115 mm.

Fig./7/a11ows for easily determining the a11owab1e 10ad taken by a masonry 1inte1 as a function of 1ength, height, and width, respective1y.

zulq [kN/mJ

1" Azul q ~ ----'-_ l 1

5 O I I --.---, grenz q =479 kN (h = 112,4)' m

40,-

30

20 If 1intel width

10 multiply lul q

0,5 1,0 1,5 2,0 2,5 3.0 1 [mJ

Figure 7. Admissib1e shear 10ad of 1inte1

STRUCTURAL DETAILING

h

b " 115 llITl

b by-115

To provide adequate anchoring at the supports of the 1inte1 the tension force

FsR 0,75 max Q + N < max M k ·h

l

resu1ting in a minimum required amount of stee1

with

or

BS BS

erf As

i s determi ned.

erf As FsR

B s 24,0 N/mm~ (BSt 420 S) 28,6 N/mm (BSt 500 S)

design amount of stee1, whichever is the greater 3

( 19)

(20)

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The bond length required between the edge of the support and the end of the rebar is

12 ~ 1 > 6 d > 40 mm 3 1 s -

(21 )

\'iith bar diameter basic bond length of reinforcement in concrete taken from tab 1 e 2

The support length of the lintel lA (cf. fiC]. 1) shall be at least 115 mm, the lintel shall be supported on a mortar layer. During construc­tion auxiliary supports at a maximum of 1,25 m centers shall be provided; the supports shall not be removed until the masonry compression zone of lintel has been sufficiently hardened and cured. This can be generally assumed to have happened within a week's time. Parallel placing of more than one tension flanges is possible if the width of the masonry compres­sion is not less than the sum of the widths of the flanges.

TABLE 2 Basic bond length l} of reinforcing steel rods in concrete according

to the German Code of practice for concrete structures 131

rebar Basic bond length 11 [mm] for diameter concrete strength classes

d B 25 B 35 B 45 B 55 s [mm]

6 200 170 140 120 8 270 220 180 160

10 340 280 230 200 12 400 330 280 240 14 470 390 320 280 16 540 440 370 320 18 600 500 420 360 20 670 550 400 400

EXAMPLES DF STRUCTURAL DESIGN

In two examples the practical design of masonry lintels using the design method developed in this paper is demonstrated (fig. 8).

POSo 1 Lintel at third floor level:

Sum of loads including floor and roof supports span (cf. fig o 1) given effective height (The concrete floor may be structurally used but not the masonry wall on top .) width (excluding the insulation material)

vorh q 1 h

b'

22,0 kN/m 1,78 m

660 - 105 = 555 mm

240 - 60 180 mm

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cross section poso 1

(j)

~~ I f

l 5,0 l 5,0 l 1 1 1

I I [ml

Pos.l 1)0 Figure 8 . Design example

Pos.2 2,18

Shear design

From figo 7 for 1 and h is obtained::

zu 1 q 22. 18 34,4 kN/m :> vorh q

Flexural design

Acting moment

from table 1:

steel required

M

kh

ks

erf AS

11,5

22,0 • 1,782/8

55,5N 8,7 / 0,18

4,55 (BSt 420 S)

4,55 • 8,7/55,5

design amount of stee1 2 0 10 mm ~ 1, 6 cm2

Structural detailing

8,7 kNm

8,0

k z = 0,92

0,7 cm2

FsR

= 0,75' 22,0' 1,78 2

14,7 kN ~ 8,7 0,92 • 0,555

17,0 kN

IA [m]

0,12

0,12

LO

tIl

'"

--r

'"

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erf AS = 14,7 /2 4 0,61 em2 , max AS/3 0,53 em2

minimum bond 1ength of rebars

0,61 , 34 em 1,6

8,6 em 7 6 . 1, O em

12 7 - em

3

chosen support 1engt h of 1inte1 = 120 mm . Auxi1iary support at mid-span of 1inte1.

Poso 2 Lintel at first floor level:

Sum of loads vorh q = 71,0 kN/m

Cross seet ion: in analogy to Po s o 1 wit h 2 U-shaped units havin g a wid th of 175 mm and a 15 mm insulation in between .

Shear design

Vir tual load

Henee, b' = 365 - 60 = 305 mm span 1 = 2,18 + 0 ,08 = 2,26 m

q' 71 ,O • ~6',~ = 26 o kN / , :J m,

from fig o 7 for q and 1 the required effeetive height h ~ 760 ·mm ehosen h ~i ght = 805 mm whieh equals 4 eou rses above tension flange.

Flexural design

Ae ting moment

from table 1

steel requi red

desig n amount

of steel

Structural detailing

M 71,0 • 2,26 2/8 = 45,3 kNm

kh 80,5/\/ 45,3 / 0,305 = 6,6

ks 4,67 (BSt 420 S); ~z 0,89

erf AS = 4,67 • 45,3/80,5 = 2,6 em2

2 0 10 mm eaeh U-shape - 3,1 em 2

0,75' 71, O - 2,26 2

60,0 kN == 45,3 63,2 kN

0,89 -0,805

erf AS 60,0 / 24

minimum bond length of rebars

12

2 • 1,0 • 3

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0.2 . 34 em 3,1

18,2 em 7 6 • 1, O > ]1 em 3

ehosen support length of lintel = 200 mm (must exeeed bond length of re­bars). Auxil iary support at mid -span of lintel.

REFERENCES

/ 1/ German Institute for Standardization, Richtlinie für die Bemessung

und Ausführung von Flachstürzen, Mauerwerk-Kalender 1980, Ernst & Sohn,

Berlin, p . 469-475.

/2/ Ohler, A., Bemessung von Flachstürzen, Mauerwerk-Kalende r 1988, Ernst

& Sohn, Berlin, p. 497-505.

/ 3/ German Institute for Standardization, OIN 1045 - Beton- und Stahlbe­

ton, Bemessung und Ausführung, Beton-Kalender 1987, Teil ~, Ernst

& Sohn, Berlin, p. 164-260.

/ 4/ Leonhardt, F. , Vorlesung über Massivbau, Teil 1, Springer-Verlag 1973.

/ 5/ Sehubert, P., and Glitza. H., E-Modul-Werte, Querdehnungszahlen und

Bruchdehnungswerte von Mauerwerk, Oie Bauteehnik 1981, No. 6,

p. 181-185.

/ 6/ Metje, W.-R., Zum EinfluB der Steinfeuchtigkeit bei der Verarbeitung

auf das Trag- und Verformungsverhalten von Mauerwerk, Mitteilungen

~ dem Institut für Baustoffkunde und Materialprüfung TU Hannover,

No . 50, 1983.