**Analysis of a Two-Story Frame in Structural Engineering**This educational document examines the analysis of a two-story frame braced in the y-axis (Ky=1) and connected as a moment frame for the x-axis. The material used is steel with a yield strength, Fy, of 50 ksi. This analysis focuses on determining several key parameters for column BF in the structure.### Objectives:a) **Kx for Column:** - Determine the effective length factor (Kx) for the column BF.b) **Governing Buckling Axis:** - Identify which axis is critical for buckling.c) **Failure Mode:** - Categorize the mode of failure as inelastic or elastic global buckling.d) **Design Strength:** - Calculate the design strength of the column using the Load and Resistance Factor Design (LRFD) method (ϕPn).e) **Adequacy for Service Loads:** - Check if the column can withstand a service dead load of 180K and a live load of 240K.f) **Replacement Column:** - Use the Kx value obtained in part (a) to find and compare the weight of the lightest Hollow Structural Section (HSS) rectangular section that can replace the W12x72.### Structural Diagram:The diagram illustrates a two-story frame with the following specifications:- **Beams and Girders:** - Top Story (I-J-K-L): W18 x 35, W18 x 40 - Middle Beam (E-F-G-H): W18 x 35- **Columns:** - BF: W12 x 72 - Other columns: W12 x 50- **Dimensions:** - Width of each bay: 20 feet and 30 feet - Heights: 20 feet (top story), 15 feet (bottom story)The frame is connected to a stable ground as shown at points A, B, C, and D. It includes a moment frame and is visually outlined with fixed and pinned connections, typically used in frame analysis for stability and support considerations.

Given: Column BF: L = 15 ft fy = 50 ksi ky = 1 Section properties: W 12 x 72 rx = 5.31 in ry = 3.04 in Ag = 21.1 in2 Weight = 72 lb/ftSolution: Calculate the effective length: For the column, the ends are pinned and fixed. k = 0.8, Since ky = 1 is given for x axes use kx = 0.8 Lx = 15 ft Ly = 15 ft Therefore; kxLx=0.8×15=12 ftkyLy=1×15=15 ftDetermine the governing slenderness ratio: Major axis slenderness ratio: λx=kxLxrx=12×125.31=27.1 Minor axis slenderness ratio: λy=kyLyry=15×123.04=59.21Calculate the buckling strength for governing slenderness ratio: The governing slenderness ratio is the larger of λx, λy λy is larger and the governing slenderness ratio; λc=kyLyryfyE=59.215029000=2.45λc>1.5 Therefore; Fcr=0.877λc2fy=0.8772.452×50=7.31 ksi Fcrfy=7.3150=0.15 Long columns (large KL/r) usually fail by elastic bucklingCalculate the column strength: KL=kyLyrx/ry=15×125.31/3.04=103.05=8.6 ft From table 4-2 for KL = 9 ft ϕFcr=44.7 ksi Design column strength: ϕPn=ϕFcrAg=44.7×21.1=943.17 kips Check the adequacy of the column: Pu=1.2DL+1.6LL=1.2×180+1.6×240=600 kipsPu>ϕPn Hence the column is adequate.Select the lightest HSS rectangular section: Ag, requored=1.1×Pufy=1.1×60050=13.2 in2 Use HSS 12 x 8 x 1/2 Ag = 17.2 in2 rx = 4.41 in ry = 3.21 in weight = 62.33 lb/ft Slenderness ratio: kLrmin=0.8×15×123.21=44.86 From table 4 -14 ϕFcr=39.1-39.9-38.844.86-4445-44=38.842 ksi Design strength: ϕPn=ϕFcrAg=38.84×17.2=668.1 kipsϕPn>Pu Hence the section is OKa) kx = 0.8 b) The λy is larger and the governing buckling about the y axis c) Elastic global buckling failure mode in column d) The design column strength is ϕPn=943.17 kips e) The column is adequate f) The lightest HSS rectangular section HSS 12 x 8 x 1/2, the weight of the selected section is lighter when compared to the W sections

Engineering

Civil Engineering

A two-story frame, is braced in y axis (Ky=1) and is connected as moment frame for x axis as shown below. Assuming elastic behavior, and all steel has Fy-50ksi, determine following for column BF. a) Kx for column. b) The governing buckling axis. c) Failure mode in column (Inelastic or elastic global buckling). d) Design strength of the column according to LRFD method (Pn). e) If the column is adequate for the service dead load of 180K and live load of 240K. f) Use the kx value obtained in part a and select lightest HSS rectangular to replace W12x72. Compare the weight of selected section E A W18 X 35 W18 X 35 F 20' B W12 X 50 W12 X 72 W18 X 40 W18 X 50 30' G K 30' H 20' 15'

A two-story frame, is braced in y axis (Ky=1) and is connected as moment frame for x axis as shown below. Assuming elastic behavior, and all steel has Fy-50ksi, determine following for column BF. a) Kx for column. b) The governing buckling axis. c) Failure mode in column (Inelastic or elastic global buckling). d) Design strength of the column according to LRFD method (Pn). e) If the column is adequate for the service dead load of 180K and live load of 240K. f) Use the kx value obtained in part a and select lightest HSS rectangular to replace W12x72. Compare the weight of selected section E A W18 X 35 W18 X 35 F 20' B W12 X 50 W12 X 72 W18 X 40 W18 X 50 30' G K 30' H 20' 15'

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Design criteria for structural loading

The different loads such as loads due to self-weight (dead load) and external loads such as live load, wind loads, seismic load, snow load, and other loads and load combinations that influence the design of a building are called structural loading. The nature of the applied load differs from changes in the location, design, and type of materials used. The design criteria require that structures must be designed and constructed to be able to withstand all load types that are expected to act upon the structure and render its usage for the designated purpose. The structural members such as beams, slabs, columns, and foundations help the structure to withstand the applied load. There are different institutes such as ASCE and ACI that provide building design codes to assure minimum safety requirements and quality of the structures.

Question

**Analysis of a Two-Story Frame in Structural Engineering**

This educational document examines the analysis of a two-story frame braced in the y-axis (Ky=1) and connected as a moment frame for the x-axis. The material used is steel with a yield strength, Fy, of 50 ksi. This analysis focuses on determining several key parameters for column BF in the structure.

### Objectives:

a) **Kx for Column:**
- Determine the effective length factor (Kx) for the column BF.

b) **Governing Buckling Axis:**
- Identify which axis is critical for buckling.

c) **Failure Mode:**
- Categorize the mode of failure as inelastic or elastic global buckling.

d) **Design Strength:**
- Calculate the design strength of the column using the Load and Resistance Factor Design (LRFD) method (ϕPn).

e) **Adequacy for Service Loads:**
- Check if the column can withstand a service dead load of 180K and a live load of 240K.

f) **Replacement Column:**
- Use the Kx value obtained in part (a) to find and compare the weight of the lightest Hollow Structural Section (HSS) rectangular section that can replace the W12x72.

### Structural Diagram:

The diagram illustrates a two-story frame with the following specifications:

- **Beams and Girders:**
- Top Story (I-J-K-L): W18 x 35, W18 x 40
- Middle Beam (E-F-G-H): W18 x 35
- **Columns:**
- BF: W12 x 72
- Other columns: W12 x 50
- **Dimensions:**
- Width of each bay: 20 feet and 30 feet
- Heights: 20 feet (top story), 15 feet (bottom story)

The frame is connected to a stable ground as shown at points A, B, C, and D. It includes a moment frame and is visually outlined with fixed and pinned connections, typically used in frame analysis for stability and support considerations.

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