# Reinforcement of Existing Column in RFEM per AISC Design Guide 15

### Technical Article

Sometimes a structure needs reinforcement in cases where a new floor being added, or when an existing member is found to be under design due to hard-to-predict loading assumption. In many cases, the structural member may not be easily replaced, and reinforcement is implemented to meet the new loading requirement.

This article demonstrates the use of "Parametric-Thin-Walled" cross-section available in RFEM based on the LRFD example shown in AISC Design Guide 15: Rehabilitation and Retrofit [2]. The RF-STEEL AISC add-on module is used to perform the design check for both the unreinforced and reinforced columns according to AISC chapter E.

Shown below is example 6.2 of AISC Design Guide 15 [2], where the AISC historic shape W10X66 (F_{y} = 33 ksi) is used for the 16 ft long column.

The following steps outline the procedure of creating user-defined cross-section and material.

#### Create the user-defined W10X66 cross-section

- Choose the "Symmetric I-Section" in the Cross-Section Library. Then enter the geometric properties found on Table 5-2.1 (page 50 of Design Guide 15 [2]). The next step is to create a new user-defined material for F
_{y}= 33 ksi steel using the [Import Material from Material Library] button. - Fill out the filter in Material Library, then "Create New Material" based on "Steel A36". In the next window, fill in the "Material Description" and revise F
_{y}to 33 ksi. - Draw the 16 ft long member. Provide pinned support (Z-rotation fixed) at the bottom of column. For the support at the top, only translation is fixed in the X and Y directions. Apply axial load = 550 kips (Dead + Live).
- Solve the model using the add-on module RF-STEEL AISC.

As shown above, the required strength exceeds the available strength by 26 %, and therefore the column requires reinforcing steel plates (F_{y} = 36 ksi) welded to the column flanges. Assume that the reinforcing plates are installed over the entire column length.

Note: The minor discrepancies in compressive strength between RFEM model and AISC hand-calculation example [2] is due to the difference in cross-sectional areas (corner radius is not included in RFEM cross-section).

#### Create the user-defined Reinforced W10X66 column with A36 Steel Plates

The welded reinforcing plates will increase both the area and the moment of inertia of the column. This will result in an increased compressive strength as determined from AISC Specification Section E3 [1].

The design of reinforcement is an iterative process best done using a spreadsheet. This solution will present only the final solution, where two 3/8 in thick x 8 in wide cover plates are welded to the column flanges as shown below.

- Choose the "Strengthened I-Section" in the Cross-Section Library. Then enter the geometric properties of the W10x66 column and the 3/8 in. x 8 in. reinforcement plates. Pick the same user-defined material "Steel Fy=33" that was previously created (Per AISC Design Guide 15 [2], "The existing column has a yield strength of F
_{y}= 33 ksi, while the reinforcing plates have a yield strength of F_{y}= 36 ksi. For the calculation of the available compressive strength of the column, conservatively consider a yield strength of 33 ksi for the entire reinforced column cross section."). - Repeat the same procedure of drawing the column and applying loads as shown previously. Solve the model using RF-STEEL AISC. As shown below, the reinforced column meets the design code check.

#### Check the requirements for built-up columns per AISC section E6 and design the welds

From AISC Specification section E6.1 [1], the connections at the ends of the reinforcing plates are designed for the full compressive load within the plate. Design the end connections for the yield strength of the reinforcing plates.

Use 1/4 in. fillet welds on both sides of the reinforcing plate. The flange thickness is t_{f} = 0.748 in. and the reinforcing plate is 3/8 in. thick, thus the weld size meets the minimum size requirements of AISC Specification Table J2.4 [1]. The required weld length is:

${\mathrm{l}}_{\mathrm{weld}}=\frac{{\mathrm{P}}_{\mathrm{u}}}{(2\mathrm{welds})\cdot \left({\mathrm{\varphi R}}_{\mathrm{n}}\right)}\phantom{\rule{0ex}{0ex}}{\mathrm{l}}_{\mathrm{weld}}=\frac{{\mathrm{F}}_{\mathrm{y}}\xb7{\mathrm{A}}_{\mathrm{g}}}{(2\mathrm{welds})\xb7\left({\mathrm{\varphi R}}_{\mathrm{n}}\right)}\phantom{\rule{0ex}{0ex}}{\mathrm{l}}_{\mathrm{weld}}=\frac{108.0\mathrm{kips}}{(2\mathrm{welds})\xb7(5.57\mathrm{kips}/\mathrm{in})}\phantom{\rule{0ex}{0ex}}{\mathrm{l}}_{\mathrm{weld}}=9.70\mathrm{in}\to \mathrm{use}10.0\mathrm{in}$

l_{weld} |
Length of weld |

P_{u} |
Compressive load of (1) plate = F_{y} . A_{g} |

F_{y} |
Yield strength of plate = 36 ksi |

A_{g} |
Gross area of (1) plate = 0.375 in x 8.0 in = 3.0 in^{2} |

ΦR_{n} |
Weld design strength per inch of weld |

This weld length meets the prescriptive requirement from AISC section E6.2(b)[1] that the end weld length not be less than the maximum width of the member.

Use 1/4" weld x 10 in long longitudinal welds on both sides at the ends of the plates.

From AISC section E6.1(b) [1], a modified slenderness ratio for built-up columns is required when a/ri > 40, where a is the distance between welds. To avoid the need to use a modified slenderness, the maximum distance between intermittent fillet welds should be limited to:

${\mathrm{r}}_{\mathrm{i}}=\sqrt{\frac{{\mathrm{I}}_{\mathrm{xi}}}{{\mathrm{A}}_{\mathrm{i}}}}=\sqrt{\frac{0.0352{\mathrm{in}}^{4}}{3.0{\mathrm{in}}^{2}}}=0.108\mathrm{in}\phantom{\rule{0ex}{0ex}}{\mathrm{a}}_{\mathrm{max}}=40{\mathrm{r}}_{\mathrm{i}}=40\xb70.108\mathrm{in}=4.33\mathrm{in}\to \mathrm{use}4.0\mathrm{in}$

r_{i} |
Radius of gyration of (1) plate |

I_{xi} |
bt^{3}/12 = [(8.0in) . (0.375in)^{3}]/12 =0.0352in^{4} (one plate) |

A_{i} |
Area of (1) plate = t w = (0.375in)(8in) = 3.0in^{2} |

a_{max} |
Maximum distance between intermittent fillet welds |

Use intermittent connecting welds 1.5 in. long at 4 in. on center (section J2.2b for minimum weld length). 1.5 in long weld meets the 4*weld size and 1.5 in minimum.

From AISC section E6.2(a) [1], the individual components of compression members must be connected at intervals, a, such that the slenderness ratio, a/r_{i}, does not exceed 3/4 times the governing slenderness ratio of the built-up member.

$\frac{\mathrm{a}}{{\mathrm{r}}_{\mathrm{i}}}=\frac{4.0\mathrm{in}}{0.108\mathrm{in}}=37.0\phantom{\rule{0ex}{0ex}}\frac{3}{4}\left(\frac{{\mathrm{L}}_{\mathrm{c}}}{{\mathrm{r}}_{\mathrm{o}}}\right)=\frac{3}{4}\left(\frac{192\mathrm{in}}{2.529\mathrm{in}}\right)=57.137.0\mathrm{o}.\mathrm{k}.$

a |
Weld intervals |

r_{i} |
Radius of gyration of (1) plate |

L_{c} |
Unbraced length of column = 16 ft = 192 in |

r_{o} |
Minimum radius of gyration of the reinforced section (r _{z} in RFEM) |

From AISC section E6.2(b) [1], the maximum spacing of intermittent welds shall not exceed the plate thickness times 0.75 √(E/F_{y}), nor 12 in.

$\mathrm{t}\left\{0.75\sqrt{\frac{\mathrm{E}}{{\mathrm{F}}_{\mathrm{y}}}}\right\}=(0.375\mathrm{in})\left\{0.75\sqrt{\frac{29,000\mathrm{ksi}}{36\mathrm{ksi}}}\right\}=7.98\mathrm{in}4.0\mathrm{in}\mathrm{o}.\mathrm{k}.$

t |
Plate thickness |

E |
Modulus of elasticity |

F_{y} |
Yield strength of reinforced section |

Final design of the reinforced column is shown below.

As shown from the above example, RFEM "Parametric-Thin-Walled" cross-section can be utilized to calculate the geometric properties of commonly used built-up members. The add-on module RF-STEEL AISC calculates the member's design strengths and perform code check.

#### Author

#### Cisca Tjoa, PE

Customer Support & Marketing

Cisca provides technical support for Dlubal Software customers and contributes to the marketing outreach throughout North America.

#### Keywords

AISC AISC 360-16 Column Reinforced Column

#### Reference

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In the case of open cross -sections, the torsional load is removed mainly via secondary torsion, since the St. Venant torsional stiffness is low compared to the warping stiffness.

SHAPE-THIN | Cold-Formed Sections

SHAPE-THIN determines the effective cross-sections according to EN 1993-1-3 and EN 1993-1-5 for cold-formed sections. You can optionally check the geometric conditions for the applicability of the standard specified in EN 1993‑1‑3, Section 5.2.

The effects of local plate buckling are considered according to the method of reduced widths and the possible buckling of stiffeners (instability) is considered for stiffened sections according to EN 1993-1-3, Section 5.5.

As an option, you can perform an iterative calculation to optimize the effective cross-section.

You can display the effective cross-sections graphically.

Read more about designing cold-formed sections with SHAPE-THIN and RF-/STEEL Cold-Formed Sections in this technical article: Design of a Thin-Walled, Cold-Formed C-Section According to EN 1993-1-3.

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