**3.3. Twenty-story space frame**

86 Advances in Computational Stability Analysis

P/2

3P

P

AA

Z Y

O

**Figure 13.** Two-story space frame

0

30

60

Applied load, P (kN)

90

120

150

400 cm

X

**Figure 14.** Load- displacement curves of two-story space frame

P

3P

B

2P 2P

u

P P

P/2

2P 2P

P/2 P/2

B

20 cm

E = 19,613 MP y = 98 MPa = 0.17

300 cm

400 cm

400 cm

P/4

P/2

P/2

P/4

0 20 40 60 80 100 120 Horizontal displacement, u (cm)

Present (fiber model)

De Souza (2000)

ABAQUS (5 element/member) ABAQUS (50 element/member) Present (refined plastic hinge model)

20 cm

40 cm

40 cm

A-A

B-B

The last example is a large scale twenty-story space steel frame as shown in Fig. 15. The aim of this example is to demonstrate the capability of two proposed methods in predicting the strength and behavior of large-scale structures. A50 steel with yield stress of 344.8 Mpa, Young's modulus of 200 Gpa, and Poisson's ratio of 0.3 is used for all sections. The load applied to the structure consists of gravity loads of 4.8 kN/m2 and wind loads of 0.96 kN/m2 acting in the Y-direction. These loads are converted into concentrated loads applied at the beam-column joints. The obtained results are also compared with those generated by Jiang et al. (2002) using the mixed element method.

Jiang et al. (2002) used both the plastic hinge and spread-of-plasticity elements to model this structure to shorten the computational time because the use of a full spread-of-plasticity analysis is very computationally intensive. When a member modeling by one plastic hinge element detected yielding to occur between the two ends, it was divided into eight spreadof-plasticity elements to accurately capture the inelastic behavior. In this study, each framed member is modeled by only one proposed element. The load-displacement curves of node A at the roof of the frame obtained by the present elements and mixed element of Jiang et al. (2002) are shown in Fig. 16. The ultimate load factor of the frame is also given in Table 2. A very good agreement between the results is seen.


**Table 2.** TAnalysis result of twenty-story space frame

Advanced Analysis of Space Steel Frames 89

**Figure 16.** Load-displacement curves of twenty-story space frame

shown in the works of Thai & Kim (2011a).

This chapter has presented two advanced analysis methods for space steel frames. In these methods, the geometric nonlinearities are captured using the stability functions, while the material nonlinearities are considered using the refined plastic hinge model and fiber model. The benefit of using the stability functions is that they require only one element per member, and hence, minimize the modeling and solution time. The advantage of refined plastic hinge model is its simplicity and efficiency. However, it is limited to steel material. Although the fiber model is a little bit time consuming compared to the refined plastic hinge model, it can be used for both steel and concrete or concrete-filled steel tubular structures as

0 0.005 0.01 0.015 0.02 0.025 0.03 Roof displacement at node A in the Y-direction/Building height

Jiang et al. (2002)

Present (fiber model)

Present (refined plastic hinge model)

[1] AISC. (2005). *Load and resistance factor design specification for structural steel buildings,*

[2] Batoz, J. L. & Dhatt, G. (1979). Incremental displacement algorithms for nonlinear problems. *International Journal for Numerical Methods in Engineering*, Vol. 14, No. 8, pp.

American Institute of Steel Construction, Chicago, Illinois.

**4. Conclusion** 

0

0.2

0.4

0.6

Load factor

0.8

1

1.2

**Author details** 

*Hanyang University, South Korea* 

Huu-Tai Thai

**5. References** 

1262-1297.

**Figure 15.** Twenty-story space frame

**Figure 16.** Load-displacement curves of twenty-story space frame

## **4. Conclusion**

88 Advances in Computational Stability Analysis

**Figure 15.** Twenty-story space frame

This chapter has presented two advanced analysis methods for space steel frames. In these methods, the geometric nonlinearities are captured using the stability functions, while the material nonlinearities are considered using the refined plastic hinge model and fiber model. The benefit of using the stability functions is that they require only one element per member, and hence, minimize the modeling and solution time. The advantage of refined plastic hinge model is its simplicity and efficiency. However, it is limited to steel material. Although the fiber model is a little bit time consuming compared to the refined plastic hinge model, it can be used for both steel and concrete or concrete-filled steel tubular structures as shown in the works of Thai & Kim (2011a).

### **Author details**

Huu-Tai Thai *Hanyang University, South Korea* 

### **5. References**


*[3]* De Souza, R. (2000). Force-based finite element for large displacement inelastic analysis of frames. PhD Dissertation, *Department of Civil and Environmental Engineering, University of California at Berkeley.* 

**Chapter 5** 

© 2012 Cuhadaroglu et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Analytical, Numerical and Experimental** 

**Compression Members with Pinned Ends** 

In earthquake resistant structural steel design, there are two commonly used structural systems. "Moment resisting frames" consist of beams connected to columns with moment resisting (i.e., rigid) connections. Rigid connection of a steel beam to a steel column requires rigorous connection details. On the other hand, in "braced frames", the simple (i.e., pinned) connections of beams to columns are allowed since most of the earthquake forces are carried by steel braces connected to joints or frame elements with pinned connections. The load carrying capacity of a braced frame almost entirely based on axial load carrying capacities of the braces. If a brace is under tension in one half-cycle of an earthquake excitation, it will be subjected to compression in the other half cycle. Provided that the connection details are designed properly, the tensile capacity of a brace is usually much higher than its compressive capacity. In fact, the fundamental limit state that governs the behavior of such steel braces under seismic forces is their global buckling behavior under compression.

After detailed evaluation, if a steel braced structure is decided to have insufficient lateral strength/stiffness, it has to be strengthened/stiffened, which can be done by increasing the load carrying capacities of the braces. The key parameter that controls the buckling capacity of a brace is its "slenderness" (Salmon et al., 2009). As the slenderness of a brace decreases, its buckling capacity increases considerably. In order to decrease the slenderness of a brace, either its length has to be decreased, which is usually not possible or practical due to architectural reasons, or its flexural stiffness has to be increased. Flexural stiffness of a brace can be increased by welding steel plates or by wrapping fiber reinforced polymers around the steel section. Analytical studies (e.g., Timoshenko & Gere, 1961) have shown that it

and reproduction in any medium, provided the original work is properly cited.

**Studies on Stability of Three-Segment** 

Seval Pinarbasi Cuhadaroglu, Erkan Akpinar,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/45807

**1. Introduction** 

Fuad Okay, Hilal Meydanli Atalay and Sevket Ozden

