31 July 20206 August 2020 by Omotoriogun Victor

The Truth About Concealed Concrete Beams

Concealed concrete beams are beams whose depth are kept equal to the thickness of the supported slab. They are normally reinforced separately from the slab, having longitudinal bars and stirrups like a normal drop beam. Sometimes they’re referred to as “hidden or strong band beams” and are provided in concrete framed structures purely due to aesthetic concerns.

Figure 1: Concealed Beam in a Solid Slab

Conventional drop beams are known to frequently interrupt floor clearance and generally impair the aesthetics of buildings structures in certain instances. For example, where a beam is required between the interface of a lounge and the dining of a residential building or generally where a clear span with open space is required. Adopting a drop beam would obviously reduce the headroom and may likely affect the aesthetic requirement of the structure. Thus, in such instances, a concealed beam is one of the possible solution available.

Application of Concealed Beams

The concept of concealed beams is an extension of the concept of flat slabs and have been found to be very efficient. By providing a concealed beam, increased headroom, clear way for electromechanical ducts and aesthetic appearance of the finished building is enhanced. Generally, most of the advantages of flat slabs are also available to concrete slabs with concealed beams.

However, concealed beams should be used only in certain instances, as a matter of fact, nobody wakes up to start designing concealed beams. They are very unconventional and required only in certain instances due to strict and very rigid architectural arrangement.

As mentioned earlier in this post, the primary purpose of a concealed beam is for aesthetic purposes. More importantly, they are useful where a long-span slab is required to support point loads or line loads e.g. from block wall partitions. Concealed beams are equally used to break up a very wide slab panel to smaller sizes where drop beams are non-viable.

However, they are grossly uneconomical when compared with drop beams due to the cost of construction as a result of the high quantity of steel required in the beams.

Design of Concealed Beam

Designing a concealed beam is the same process as for conventional drop beams, with the only difference being that the beam depth is restricted to that of the supported slab. As a result of this restriction, the width of the beam is usually very wide and heavily reinforced in order to compensate for the loss in stiffness and control deflection which is always very critical.

Some engineers hold the view that a concealed beam does not behave like a beam but rather like a slab. This is a complete fallacy which stems from the stereotype that a beam must be considerably deep relative to its width in order to function as a beam.

A Concrete Beams is an Element whose width is less than 5 times its depth in other instances it’s a slab and should be treated as such
IstructE- Technical Guidance Note on Concrete Beams

However, even the technically most advanced codes of practice do not define structural elements in terms of cross-section, only the behaviour of structural elements are emphasized. Thus, from this perspective, the behaviour of a slab and beam is no different. they are designed for flexure, shear, deflection the same way.

As long as all checks are performed and found to be satisfactory, a beam will function irrespective of its size. However, there have been reports of some designers using concealed beams in extremely thin slabs even when the check for deflection can not be satisfied. This is extremely wrong, especially if the concealed beam is considered a principal structural element in the analysis and design. But, for safety concerns only, concealed beams may be used as local stiffeners for strengthening the slabs at locations where line loads/point loads are applied.

See: Designing a Concrete Beam to Eurocode

Worked Example

Figure 3 shows a very wide interior panel of a solid slab in a reinforced concrete framed structure. It is required to carry line loads from permanent partition walls at 4.00m centres. More so, it is required to break up the wide panel into smaller sizes without the use of drop beams. Design a concealed beam within the panel using grade 30/37 concrete and 500Mpa steel bars completely.

Actions

Permanent actions:

self\quad weight\quad of\quad slab\quad =0.25\times 25=6.25kN/{ m }^{ 2 }

finishes\quad \& \quad services\quad say\quad =1.5kN/{ m }^{ 2 }

permanent\quad actions\quad { g }_{ k }=\quad 7.75kN/{ m }^{ 2 }

Variable actions:

floor\quad imposed\quad load\quad (offices)\quad =\quad 2.5kN/{ m }^{ 2 }

demountable\quad partitions\quad say\quad =\quad 0.5kN/{ m }^{ 2 }

variable\quad actions\quad { q }_{ k }=3.0kN/{ m }^{ 2 }

Design value of actions: By inspection, the permanent actions are less than 4.5 times the variable action, hence equation 6.10b of BS EN 1990 is critical

{ n }_{ s }=1.35\xi { g }_{ k }+1.5{ q }_{ k }

(1.35\times 0.925\times 7.75)\quad +(1.5\times 3)=14.18kN/{ m }^{ 2 }

UDL on concealed beams:

load\quad transfered\quad to\quad beams\quad =2\times \frac { { n }_{ s }{ l }_{ x } }{ 6 } \left[ 3-\left( \frac { { l }_{ x } }{ { l }_{ y } } \right) ^{ 2 } \right]

=2\times \frac { 14.18\times 4 }{ 6 } \left[ 3-\left( \frac { 4 }{ 6 } \right) ^{ 2 } \right] =48.32kN/m

wall\quad loads\quad =\quad 12.5kN/m

Total\quad udl\quad on\quad beam\quad =\quad 48.32+12.5=60.82kN/m

Structural Analysis

{ M }_{ max }={ M }_{ Ed }=\frac { w{ l }^{ 2 } }{ 8 } =\frac { 60.82\times { 6 }^{ 2 } }{ 8 } =273.7kN.m

{ V }_{ max }=\frac { wl }{ 2 } =\frac { 60.82\times 6 }{ 2 } =182.5kN

Flexural Design

{ M }_{ Ed }=273.7kN.m

assuming\quad cover\quad 25mm,\quad 16mm\quad bar\quad and\quad 8mm\quad links

d=h-\left( c+\phi /2+links \right) \quad =250-(25+16/2+8)=209mm

{ b=b }_{ eff }={ b }_{ eff,1 }+{ b }_{ w }+{ b }_{ eff,2 }

where\quad { b }_{ eff,i }=\quad { 0.2b }_{ i }+{ 0.1l }_{ o }\le 0.2{ l }_{ o }\le { b }_{ i }

{ b }_{ 1 }=\frac { 4000-150-600 }{ 2 } =1625mm

{ b }_{ 2 }=\frac { 4000-600-600 }{ 2 } =1400mm

{ b }_{ eff,1 }=0.2(1625)+0.1(6000)\le 0.2(6000)\le 1625\quad =925mm

{ b }_{ eff,2 }=0.2(1400)+0.1(6000)\le 0.2(6000)\le 1400\quad =880mm

b={ b }_{ eff }=925+1200+880=3005mm

k=\frac { { M }_{ Ed } }{ { bd }^{ 2 }{ f }_{ ck } } =\frac { 273.7\times { 10 }^{ 6 } }{ 3005\times { 209 }^{ 2 }\times 30 } =0.070

z=d\left[ 0.5+\sqrt { 0.25-0.882k } \right] \le 0.95d

z=0.93d\quad =0.93\times 209=194.37mm

{ A }_{ s }=\frac { { M }_{ Ed } }{ 0.87{ f }_{ y }z } =\frac { 273.7\times { 10 }^{ 6 } }{ 0.87\times 500\times 194.37} =3237.10{ mm }^{ 2 }

Use\quad 22H16\quad bars\quad -\quad 55mm\quad spacing\quad \left( { A }_{ s,prov }=4422{ mm }^{ 2 } \right)

Shear Design

The design shear force is taken at d from the support:

{ V }_{ Ed }=182.5-\left( 0.209\times 60.82 \right) =169.8kN

By inspection, shear is not critical in the beam. Therefore minimum area of shear reinforcement will be provided.

\frac { { A }_{ sw,min } }{ { s }_{ v } } =\frac { 0.08\sqrt { { f }_{ ck } } }{ { f }_{ yk } } { b }_{ w }=\frac { 0.08\sqrt { 35 } }{ 500 } \cdot 1200\quad =1.36

max.\quad spacing\quad { s }_{ v }=0.75d= 0.75(209)=156.75

Use\quad 4H8-125mm\quad centers\quad \left( 1.61 \right)

Deflection Check

{ \left[ \frac { l }{ d } \right] }_{ limiting }N\cdot K\cdot F1\cdot F2\cdot F3

\rho =\frac { { A }_{ s,req } }{ bd } =\frac { 3237.10 }{ 3005\times 209 } =0.0052%

{ \rho }_{ o }=\sqrt { 30 } \cdot { 10 }^{ -3 }=0.0055%

N=\left[ 11+\frac { 1.5\sqrt { { f }_{ ck } } { \rho }_{ o } }{ \rho } +3.2\sqrt { { f }_{ ck } } { \left( \frac { { \rho }_{ o } }{ \rho } -1 \right) }^{ 3/2 } \right]

=\left[ 11+\frac { 1.5\sqrt { 30 } \times 0.55 }{ 0.52 } +3.2\sqrt { 30 } \left( \frac { 0.55 }{ 0.52 } -1 \right) ^{ 3/2 } \right]=19.93

K=1.0\quad (simply\quad supported)

\frac { { b }_{ eff } }{ { b }_{ w } } =\frac { 3005 }{ 1200 } =2.5<3\quad F1=1.0

l<7m\quad ;\quad F2=1.0

F3=\frac { 310 }{ { \sigma }_{ s } }

{ \sigma }_{ s }=\frac { { f }_{ yk } }{ { \gamma }_{ s } } \left[ \frac { { g }_{ k }+{ \psi }_{ 2 }{ q }_{ k } }{ { n }_{ s } } \right] \cdot \left( \frac { { A }_{ s,req } }{ { A }_{ s,prov } } \right) \cdot \frac { 1 }{ \delta }

=\frac { 500 }{ 1.15 } \left[ \frac { 7.75+0.3(3) }{ 14.18 } \right] \cdot \left( \frac { 3237.1 }{ 4422 } \right) \cdot 1=194.16Mpa

F3=\frac { 310 }{ 194.16 } =1.6\le 1.5\quad 1.5

{ \left[ \frac { l }{ d } \right] }_{ limit }=\quad 19.93\times 1.0\times 1.0\times 1.0\times 1.5=29.9

{ \left[ \frac { l }{ d } \right] }_{ actual }=\frac { 6000 }{ 209 } =28.7

Since the actual span: effective depth ratio is less than the limiting span: effective depth ratio, deflection is deemed satisfactory.

Figure 3: Cross-section through Concealed Beams

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Published by Omotoriogun Victor

A dedicated, passion-driven and highly skilled engineer with extensive knowledge in research, construction and structural design of civil engineering structures to several codes of practices View all posts by Omotoriogun Victor