Yossef (2015) experimentally studied the behavior of steel-I beams by adding cover steel plates (80mmx6mm) on top as well as bottom flanges using two different patterns (i.e., only on the bottom flange and top as well the bottom flange). The beams were also provided with steel stiffeners of 6mm thickness under four-point loads (i.e., two bearing and two intermediate). Few beams were strengthened using steel plates before loading while other beams were strengthened during the loading process by a new welding technique. The beams were tested under four-point loading for determining the load-carrying capacity and deflections. The results indicated that the use of a new welding technique (used to weld cover plate while under load) for strengthening the steel beams is found to be effective in increasing the load-carrying capacity of the beams by up to 5.7% and reducing the deflection by 30.7%. The study concludes that the use of a new technique for welding cover plates to steel beams enhances the strengthening of beams.
Kaveh and Ghafari, (2018) carried out an optimization study of steel-pitched roof frames having tapered members using nine meta-heuristic algorithms taking into account different tapered lengths and apex heights. The results of the study showed that it is possible to change the optimum weight of the structure by up to 10% by selecting the tapered length and apex height of the steel-pitched roof frame.
Atwal et al., (2017) analyzed and designed a PEB (15.2m x 35m with 14m eave height) using the provisions of IS: 800–2007, American code (AISC-10), Euro code − 03, and BS5950-2000 for determining the weight of PEB. The weight of PEB obtained by using IS: 800–2007 was compared with the weights obtained by international codes (i.e. AISC-10, Euro code-03, and BS5950-2000). The results indicated that the weight of PEB gets reduced by 23.97%, 27.2%, and 9.04% when obtained by AISC-10, Euro code-03, and BS5950-2000 respectively as compared to the weight obtained by IS: 800–2000. The study recommends the use of international codes for the analysis and design of PEB.
Prabha and Emilreyan, (2018) have experimentally investigated the flexural behavior of I-sectioned steel beams (ISMB 100) strengthened by stiffeners at various positions (i.e., vertical, horizontal, and inclined stiffeners of different cross sections) along with the beam length for increasing load carrying capacity. The beams were tested under two-point loading for determining load-carrying capacity and deflections. Further, the beams were also analyzed using ANSYS software for determining load-carrying capacity and deflections considering the stiffeners similar to those provided to the beams tested experimentally. The experimental and analytical results of load-carrying capacity and deflection were compared. The analytical results are found to be validated with the results of experimentation. The results show that the load-bearing capacity and deflection increased by 41% and 15% respectively when compared with the load-carrying capacity and deflection obtained for the beams provided with W-shaped stiffeners. The study concludes that the provision of W-shaped stiffeners enhances the strength of beams.
Dahake et al., (2019) analyzed and designed a steel structure required for the installation of solar panels on the rooftop of the structure by using the provision of IS: 800–1984. The lattice trusses are provided over a single span and simply supported at the end supports on the top of the educational building. The analysis of the trusses is done by manual method of calculation. Then the steel structure is analyzed and designed on the STAAD Pro V8i software for the responses viz. displacement, shear and bending moment diagram, utilization ratio, and for total weight of the structure. Results of the responses show that all the values of responses are within the limits of IS: 800–2007. The researchers conclude that the lattice truss structure is safe and economical to construct for the installation of solar panels.
Alam and Sakalle, (2020) analyzed and designed a PEB industrial warehouse of size 24 m x 60 m having a height of 8.4 m (up to eave level) by using the provision of IS: 800–2007 and American code (AISC LRFD). The analysis was performed by using STAAD Pro software considering dead, live, wind, seismic, and snow loads. The results of the PEB are compared with the traditional steel structure for the variations in shear force, support reaction, weight, and cost of the structures. The researchers concluded that the results obtained for the responses viz. shear force and support reaction as obtained by following the guidelines of AISC LRFD are found to be lesser as compared to the results achieved by referring to the provision in IS: 800–2007.
Ridha et al., (2020) have experimentally investigated the effectiveness of strengthening steel-I beams (ISMB100) by providing vertical steel stiffeners (86mmx22mmx3mm) and inclined steel stiffeners of varying cross sections (12.5mmx3mm and 25mmx3mm) on both faces of the web. The steel plates of size 500mmx12.5mmx3mm and 500mmx25mmx3mm were also provided to the top and bottom flanges respectively. The beams were tested under single-point loading using the universal hydraulic machine (1200 kN) to determine flexural capacity and deflection. The results of the beam provided with stiffeners with additional steel plates were compared with the steel-I beams without any stiffeners and plates (control beam). From the results, researchers concluded that the stiffness of the beam provided with stiffeners and steel plates increases when compared with the stiffness of the control beam.
Gharabude and Hosur, (2020) have analyzed the behavior of steel I-beams using ANSYS software for strengthening them using steel plates and angle sections to prevent lateral buckling and torsional buckling. Five steel I-beams (ISMB150) were strengthened using specific patterns of steel plates and steel angle sections at different positions. Analysis was performed for determining lateral deflection under two-point loading. The results of the study indicated that the strengthening of beams reduces the lateral deflections of beams by 42.85% when compared with the unstrengthened beams. Researchers concluded that the strengthening of steel I-beam at its compression flange using steel plates at the intermediate point significantly reduces lateral buckling and lateral torsional buckling of steel beams.
Varma and Chandak, (2022) have analyzed and designed a pre-engineered building (21m x 45 m having a clear height- 7 m) for different parameters by using the provision of IS: 800–2007. The analysis was performed by using STAAD Pro V8i software considering dead, live, wind, collateral, solar panel loads, and load combinations. The results obtained for the responses viz. maximum shear force and maximum bending moment for positive and negative envelope was 173.901 kN and 41.017 kN respectively for beam 76 and 91.107 kN and 81.372 kN for beam 42. The possible weight for the structure is 253.796 kN when analyzed considering loads and load combinations parameters. The researchers concludes that the pre-engineered building was safe and more economical than the traditional steel building.
Analysis and design of an existing PEB structure
Analysis and design of an existing PEB structure (24 m x 36 m x, eave height-8 m) without and with the additional SL is carried out using STAAD Pro software. The geometrical and other parameters considered for the analysis and design of an existing PEB are given in Table.1.
Table 1
Geometrical details of an existing PEB structure
Parameters | Particulars |
---|
Length | 36 m |
Width | 24.86 m |
Height of the structure | 8 m |
Crane capacity | 10MT |
Height of the crane | 6 m |
Bay spacing | 7.2 m |
Location | Pune |
Type of support | Fixed support |
Wind speed | 39 m/s |
Terrain category | II |
Percentage of openings | 5% -20% |
The analysis results of both structures, i.e., without and with additional SL giving values of bending moment and bending stresses to know whether the members of PEB are safe or unsafe under the action of combined loads consisting of DL, LL, and WL with additional SL. The failed members of PEB due to these loads are identified for strengthening by considering provisions of galvanized iron (GI) plates by arranging them in specific patterns (P). The safe and failed members of PEB are identified based on the utilization ratio (UR) provided by STAAD Pro software. The UR is a ratio of the sum of all member forces to the maximum allowable forces for a particular member in the analysis. The UR less than 1.0 indicate that the design is safe. The analysis of PEB is performed using STAAD Pro software considering combined loads without and with SL as per the following steps.
-
Preparation of a 3D geometrical model of the existing PEB structure
-
Defining sectional properties to PEB members
-
Defining the combined loads (i.e., DL + LL + WL) considering without and with additional SL
-
Assigning all loads on the 3D geometrical model.
-
Analysis and design of existing PEB structure without and with additional SL
Step 1
Preparation of a 3D geometrical model of the existing PEB structure
Considering the geometrical dimensions of the existing PEB structure, a 3D geometrical model provided with fixed supports to the columns is created using STAAD Pro and is shown in Fig. 2.
Step 2
Defining sectional properties to PEB members
The columns and rafters of PEB are assigned tapered I sections of different sizes (i.e., sectional properties) and are presented in the Table. 2. Figure 3 shows the 3D-rendered view of the PEB model after assigning the sectional properties.
Table 2
Sectional properties considered for existing PEB structures
Sr. No. | PEB member | Type of section | Description of the property | Size of section (m) at node |
Start | Mid-point | End |
1. | Gable end column | Tapered I section | Depth of web | 0.550 | - | 0.650 |
Thickness of web | 0.008 | - | 0.008 |
Width of the top flange | 0.325 | - | 0.325 |
The thickness of the top flange | 0.010 | - | 0.010 |
Width of the bottom flange | 0.325 | - | 0.325 |
The thickness of the bottom flange | 0.010 | - | 0.010 |
2. | Middle Column | Tapered I section | Depth of web | 0.650 | - | 0.700 |
Thickness of web | 0.008 | - | 0.008 |
Width of the top flange | 0.350 | - | 0.350 |
The thickness of the top flange | 0.012 | - | 0.012 |
Width of the bottom flange | 0.350 | - | 0.350 |
The thickness of the bottom flange | 0.012 | - | 0.012 |
3. | Rafters | Tapered I section | Depth of web | 0.800 | 0.45 | 0.500 |
Thickness of web | 0.008 | 0.006 | 0.006 |
Width of the top flange | 0.350 | 0.250 | 0.225 |
The thickness of the top flange | 0.010 | 0.008 | 0.008 |
Width of the bottom flange | 0.350 | 0.250 | 0.225 |
The thickness of the bottom flange | 0.010 | 0.008 | 0.008 |
After assigning the sectional properties to the generated model (Fig. 2), the 3D-rendered view of the model is shown in Fig. 3.
Step 3
Defining the combined loads (i.e. DL + LL + WL) considering without and with additional SL.
The analysis of existing PEB is carried out considering combined loads (i.e. DL + LL + WL) with and without additional SL. The calculations of these loads are presented below.
-
Weight of purlin: 5 kg/m2
-
Weight of GI sheet (roofing): 5 kg/m2
-
Weight of dust: 2 kg/m2
-
Weight of solar panel (SL): 25 kg/m2
Thus, the dead load with and without SL is given below.
-
Total DL without SL: 12 kg/m2
-
Total DL with SL: 37 kg/m2
-
Total DL without considering SL on the rafter per meter length is calculated as,
Load on rafter = Total DL without SL x bay spacing
= 12 kg/m2 x7.2 m (bay spacing)
= 86.4 kg/m = 0.846 kN/m
-
Total DL with additional SL on the rafter per meter length is calculated as,
Load on rafter = Total load x bay spacing
= 37 kg/m2 x7.2 m (bay spacing)
= 273.6 kg/m = 2.722 kN/m
• Live load (LL)
Live load as per IS: 875 (Part II) for flat sloping or a curved roof with a slope up to 10o taken as 0.75kN/m2 for the analysis.
Live load per meter run on rafter = 0.75 kN/m2 x7.2m (bay spacing) = kN/m2
• Wind load (WL)
Wind load calculations as per IS: 875–2015 (Part 3)
-
Location: Pune
-
Basic wind speed Vb: 39 m/sec
-
Risk coefficient factor, k1: 1
-
Terrain roughness, Height & size factor, k2: 1 (Category 2 class B)
-
Topography Factor, k3: 1
-
Importance factor for cyclonic region, k4: 1.15 (Industrial structure)
-
Design Wind Speed, Vz = Vb x k1 x k2 x k3 x k4 = 39 x 1 x 1 x 1 x 1.15 = 44.85 m/s
-
Design wind pressure, Pz = 0.6 x (Vz)2 = 0.6 x (44.85)2 = 1206.91 N/m2 = 1.207 KN/m2
-
Wind directionality factor, Kd: 0.90
-
Area averaging factor for rafter, Ka: 0.9
-
Area averaging factor for the column, Ka: 0.9
-
Combination factor, Kc: 1
Design wind pressure for rafter, Pd = Kd x Ka x Kc x Pz = 0.9 x 0.9 x 1 x 1.207 = 0.978 kN/m2
Design wind pressure for column, Pd = Kd x Ka x Kc x Pz = 0.9 x 0.9 x 1 x 1.207 = 0.978 kN/m2
Assume internal wind pressure coefficient, Cpi :
Table 4
Wind loads acting on rafters
Wind angle | 00 | 900 |
---|
Roof Portion | EF | GH | EG | FH |
External pressure coeff. (Cpe) | -1.20 | -0.40 | -0.80 | -0.60 |
Positive internal pressure coeff. (+ Cpi) | 0.50 | 0.50 | 0.50 | 0.50 |
Negative internal pressure coeff. (− Cpi) | 0.50 | 0.50 | 0.50 | 0.50 |
Net pressure coeff. (Cpnet) considering positive pressure (Cpe–Cpi) | -1.70 | -0.70 | -1.30 | -0.30 |
Net pressure coeff. (Cpnet) considering negative pressure (Cpe–Cpi) | -0.90 | 0.10 | -1.10 | -0.10 |
Design wind pressure (Pd), kN/m2 | 0.98 | 0.98 | 0.98 | 0.98 |
Pd x (Cpnet) considering positive pressure | -1.66 | -0.88 | -1.27 | -1.08 |
Pd x (Cpnet) considering negative pressure | -0.69 | 0.10 | -0.29 | -0.10 |
Wind load (F) kN/m = Pd x (Cpnet) considering negative pressure x bay spacing | -11.97 | -6.34 | -9.15 | -7.75 |
Wind load (F) kN/m = Pd x (Cpnet) considering negative pressure x bay spacing | -4.93 | 0.70 | -2.11 | -0.70 |
Step 4. Assigning all loads on the 3D geometrical model.
In this step, the loads as calculated in the previous step 3 are assigned to the 3D model of the existing PEB (i.e. without and with SL), and the analysis of the model is performed using Staad Pro Fig. 4 (a) and Fig. 4 (b) models of PEB considering without and with SL.
Step 5. Analysis and design of existing PEB structure
The analysis and design of both the PEB models (Fig. 4a & b) considering without and with SL is performed using Staad Pro and the results of bending stresses in the columns and rafters of PEB were obtained. Based on the UR of the columns and rafters of PEB it was confirmed whether they are safe or unsafe. The analysis results confirmed that all the columns and rafters of PEB are safe under the action of combined loads without the additional SL. However, the results of the analysis of PEB considering the combined loads with additional SL confirmed that 24 columns and 30 rafters fail. Figure 5 and Fig. 6 show the safe and safe or fail members of PEB indicated by UR values (i.e. < or > 1) respectively.
The details of safe and failed members of PEB considering additional SL and their values bending stresses obtained by the analysis are presented in Table.5.
Table 5
Details of safe and failed members of PEB considering additional SL and their bending stresses
Type of member | Member no. | Length of member (m) | UR of member | Failure location of the member from the start node (m) | Bending stress (N/mm2) |
---|
Gable end column | 1 & 33 | 8.00 | 1.28 | 6.00 | 28.24 |
4 & 36 | 8.00 | 1.72 | 6.00 | 28.31 |
2,5,34,37 | 8.00 | 1.60 | 8.00 | 40.32 |
Middle column | 9 & 27 | 8.00 | 1.37 | 6.00 | 30.61 |
12 & 30 | 8.00 | 1.78 | 0.00 | 33.15 |
15 & 21 | 8.00 | 1.40 | 6.00 | 31.18 |
18 & 24 | 8.00 | 1.86 | 0.00 | 33.97 |
10,13,28,31 | 8.00 | 1.90 | 8.00 | 47.39 |
16,19,22,25 | 8.00 | 1.95 | 8.00 | 48.32 |
Rafter | 3,6,35,38 | 4.16 | 1.09 | 0.00 | 27.86 |
11,14,29,32 | 4.16 | 2.08 | 0.00 | 46.14 |
17,20,23,26 | 4.16 | 2.12 | 0.00 | 47.05 |
68 & 80 | 4.16 | 1.40 | 4.16 | 27.64 |
72 & 76 | 4.16 | 1.40 | 4.16 | 28.05 |
70 & 82 | 4.16 | 1.41 | 0.00 | 35.73 |
74 & 78 | 4.16 | 1.41 | 0.00 | 37.09 |
65 & 85 | 4.16 | 1.01 | 2.43 | 28.68 |
69 & 81 | 4.16 | 1.64 | 2.08 | 40.35 |
73 & 77 | 4.16 | 1.65 | 2.08 | 41.68 |
71 & 83 | 4.16 | 1.43 | 3.47 | 39.40 |
75 & 79 | 4.16 | 1.45 | 3.47 | 41.27 |
The variation in the bending stresses of various members of PEB considering additional SL is shown in Fig. 7.
Strengthening of failed members of PEB
The members of PEB which are failed due to the consideration of additional SL are strengthened by the provision of specific patterns of GIP at the failure locations indicated by software analysis (Ref. Table 5). For strengthening the failed members, it becomes necessary to increase the section modulus of the sections which gets increased by increasing the moment of inertia (MI) of the section. The MI of failed member sections is increased by enlarging the sections considering the additional provision of GIP in specific patterns and at particular locations. The specific patterns of GIP considered for strengthening the PEB members (columns and rafters) and their locations used in the analysis are given below.
-
Provision of GIP for columns
-
PC1: One GIP on one side flange i.e. the interior side of a column- Fig. 8 (a)
-
PC2: One GIP on each flange i.e. interior and exterior side of column-Fig. 8 (b)
-
PC3: Two GIP at each meeting place of flange and web i.e. four junctions of flange and web- Fig. 8 (c)
Figure 8 (a, b, and c) GIP patterns for PEB columns
-
Provision of GIP for rafters
-
PR1: One GIP on the bottom face of the flange- Fig. 9a
-
PR2: Two GIP at each meeting place of flange and web i.e. four junctions of flange and web -Fig. 9b
These specific patterns of GIP are generated in the ‘section wizard’ tab of STAAD Pro software and then each such pattern is assigned to the failed members (columns and rafters) of PEB. After assigning a specific pattern to the failed members the analysis and design of PEB is performed. The failed column members of PEB were provided with the three different patterns viz. PC1, PC2, and PC3 as shown in Fig. 8 (a), Fig. 8 (b), and Fig. 8 (c) respectively. Similarly, the failed rafter members of PEB were provided with two different patterns viz. PR1 and PR2 as shown in Fig. 9 (a) and Fig. 9 (b) respectively.