Design and Analysis of a Reinforced Concrete Beam Retrofitted by Externally Bonded H-Type Steel Member
BACKGROUND
For a simply supported reinforced concrete beam, the span is extended from 4m to 8m because of
removing mid-span supporting column. A concentrated load 120kN at the mid-span and a uniform load
15kN/m along the span is on the beam as shown in Figure 1.The height and width of the original beam is
500mm and 250mm. The grade of concrete is C30. Analytical results for the original reinforced concrete
beam by the current design code are listed in Table 1. Deficient flexural strength of the beam should be
strengthened. The retrofitting method of externally bonded steel plate can not be applied as the balanced
compression height of concrete may exceed the limitation. The retrofitting method of externally bonded
steel member as H10;250;10;10 by the JGN structural adhesive is suggested here as shown in Figure 2.
The area of H-type steel member AS is 5800 mm2. Treating the shadowed region in Figure 2 as the virtual
section of concrete, the effective height of the retrofitted beam is extended from 465mm to 550mm. As
the arm of tension force is extended, this retrofitting method can be applied for strengthening this beam.
This paper presents detailed works for the design and analysis of the composite beam formed by the original reinforced beam and the externally bonded H-type steel member. Three Chinese codes, as the
code for design of concrete structures (GB50010-2003), the code for design of steel structures (GB50017-
2003) and the design code for strengthening concrete structure (GB50367-2006) are involved and
abbreviated as CODE-CONCRETE, CODE-STEEL and CODE-STRENGTHENING in this paper.
Flexural Strength
CODE-CONCRETE adopts the hypothesis of rectangular compression stress distribution of concrete for
the design analysis of flexural strength of reinforced concrete beam, which is shown in Fig. 3(a). For the
restriction of the ratio of compression height vs. effective height less than 0.55, the possible maximum
flexural strength after retrofitting can be got as
Figure 3: Model for flexural strength analysis.
The stress distribution for the composite beam is assumed as Fig. 3(b). Fy , Fs , Fc are the tension force
of reinforcement, the tension force of H-type steel member and the compression force of concrete respectively. As the tension stress of H-type steel member is trapezoidal distributed, the analysis of
flexural strength for the composite beam is different from that of the reinforced concrete beam. Assuming the maximum tension stress reaches the design value s f , the resultant of the tension stress is got as\ Af ss .Here \ is the ratio of the mean value vs. the maximum value.
\ can be estimated as the ratio of effective height of the original beam vs. the retrofitted beam. For this
project, \ is estimated to be 465mm/550mmĬ0.85. Neglecting the reinforcement of the original beam,
the maximum flexural strength of the retrofitted beam is hence got as 430kNm, and the height-effective
ratio of the compression zone for concrete is 290mm/550mm=0.53. These mean satisfactory check on flexural strength by CODE-CONCRETE.
Flexural Stiffness
Shear strength
By the method of material mechanics, the shear stress analysis can be done by transforming the H-type
steel member to equivalent concrete part, as shown in the middle diagram of Figure 4. The equivalent width should be got as the width of steel member times the modulus ratio EE csE D / . For this
project, x is got as 320mm. The elastic shear stress on the composite beam is
In equation (5), Q is the shear force, S is the first moment of the area outside the check point with
respect to the neutral axis, beq is the width or equivalent width, Esceq III D . As the size of H-type steel member is small, the neutral axis is in the concrete region. The shear stress of concrete part is parabolic distributed. By integration, the total shear force of original part can be got. The partition ratio of shear force in the reinforced concrete part can be expressed as
Hence the shear strength of the composite beam can be checked, as shown in Table 3. The shear strength
of the original reinforced beam and H-type steel member is got by CODE-CONCRETE and CODESTEEL respectively. As the relative large shear strength of the H-type steel member, the shear strength of
the composite beam is determined as 195kN/0.87=225kN by the original part.
Connections
Full shear link should be set on the interface of reinforced concrete beam and the H-type steel member.
As it is a simply supported beam, the strength check of shear connector should be done according to
CODE-STEEL. The possible maximum shear force on the connector of the composite beam should be
determined as 1250kN by
Theoretical Analysis
The influence of slip for steel-concrete composite beam connected by studs can be evaluated (Nie et al.
1994; 2003). The research achievements are suggested to analyze the retrofitted beam here.
The maximum slip and the additional deflection caused by slip can be expressed as:
Finite Element Analysis
FEM (finite element method) is used for analysis on slip and deflection. The model is established, as
shown in Figure 5. Solid elements are used for concrete, JGN structural adhesive and H-type steel
member while bar elements are used for the reinforcement in concrete. The layer thickness of JGN
structural adhesive is 2mm. The anchor bolts are not considered. The uniform load 54kN/m is set on the
beam. The key parameters for concrete, steel and JGN adhesive are taken from CODE-CONCRETE, CODE-STEEL and CODE-STRENGTHENING, which are shown in Figure 6. The Poisson’s ratio is selected as 0.2 for concrete and steel, 0.25 for JGN structural adhesive.
The mid-span stress distribution along the height is shown in Figure 7. The maximum stress of concrete
in compression area is 23.8MPa and the height of compression region is about 300mm. The H-type steel
member is in elastic stage as its maximum tensile stress is 190.7MPa. The stress of JGN structural
adhesive is 19.6MPa. These means qualified results on the strength check.
Figure 8 is the result of slip and deflection along the span of the beam. The number 0 and 0.5 on the
horizontal axis represents the support and the mid-span of the beam respectively. The maximum
deflection is 19.9mm at the mid-span, which is quite near to the result in Table 2. The maximum slip is
0.014mm, which is smaller than the theoretical result 0.034mm. The main reason for the difference of slip
is that the stiffness of slip in equation (8) and (9) is obtained by the maximum slip 0.2mm and may be
underestimated. The full shear link on the interface of connection is guaranteed.
Moreover, different layer thickness of the JGN structural adhesive as 2.5mm or 1.5mm is also considered
in FEM analysis. The change of layer thickness nearly has no influence on the results. It is proved that the
stiffness of slip is mainly determined by the shear strength of the concrete.
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