CE532

Chapter 5

 

5.12 PROBLEMS

 

5.1 A W21x83 made of A36 steel with yield stress of 36 ksi is used as a simply supported beam with a span of 15 ft carrying a uniformly distributed load of intensity 5 Kips/ft including its own weight. The end supports make an inclination of 10 degrees with the horizontal, as shown in Figure 5.16. Check the adequacy of the beam according to the ASD code. Assume that the load acts through the centroid of the cross section. Lateral support is provided at the two ends of the beam only.

 


5.2 A structural tube is used as a beam to span a highway bridge of span length 32 ft. The beam is simply supported and subjected to a vertical (dead + live) load of 1 K/ft and a horizontal wind load of 60 psf acting on the face MN of the tube (Fig. 5.17). In addition to supports A and C, the beam has lateral support at the midpoint B. Using steel with yield stress of 50 ksi, select the lightest tube with a depth of 12 in.

 



5.3 A castellated beam has been built out of a W33x118 section as shown in Fig 5.18. If A36 steel is used (Fy = 36 ksi), what uniformly distributed load can this simply supported castellated beam carry for a span of 20 ft when the compression flange is braced laterally? You may not consider this beam as a compact section. How can we increase the loading capacity of this beam by only minor modifications?


 


5.4 The floor of an indoor balcony consists of W beams of length L placed at spacing of 10 ft. Each beam is connected to the column at one end through a shear connection and is supported by a hanger at a distance x from the other end (Fig. 5.19). What should the distance x be in order to obtain the minimum weight beam? Using this distance, find the lightest W shape for the beam. Use A36 (Fy = 36 ksi) and assume total lateral support. Dead and live loads of the floor are 60 psf and 100 psf, respectively. L = 30 ft.

 


5.5 The floor arrangement shown in Fig 5.20 should be designed for a live load of 100 psf and the dead load of a 6-in. reinforced concrete slab and the beam weights. Design the typical beams in the N-S direction (identified by F, G, H and I) and the girders in the E-W direction (identified by A, B, C, D and E), assuming all of them are simply supported. Use 150 pcf for the weight of concrete, Fy = 36 ksi, and assume full lateral support.

 



5.6 Solve problem 5.4, using steel with yield stress of 60 ksi.

 



5.7 The three-span continuous beam shown in Fig. 5.21 has a total length of L = 60 ft and is subjected to a distributed load of intensity q = 2 K/ft. Where should the internal supports be located (that is, find the distance x shown in the figure) in order to obtain the minimum weight beam? Assume total lateral support. Using A36 steel with yield stress of 36 ksi, find the lightest W shape for the beam.

 


5.8 Solve Problem 5.7, using steel with yield stress of 65 ksi.

 

5.9 Find the lightest W shape for the beam shown in Fig. 5.22, using A36 steel (Fy = 36 ksi) and assuming

a.    full lateral support

b.    lateral supports at points A and B only


 


5.10 Solve Problem 5.9, using steel with yield stress of Fy = 50 ksi.

 

5.11 Find the lightest S shape for the beam shown in Fig. 5.22, using A36 steel (Fy = 36 ksi) assuming

a.    full lateral support

b.    lateral supports at points A and B only

 

5.12 Solve Problem 5.11, using A572 steel (Fy = 50 ksi).

 

5.13 Find the lightest double channels for the beam shown in Fig. 5.22, using A36 steel (Fy = 36 ksi) and assuming full lateral support.

 

5.14 Find the lightest rectangular tube for the beam shown in Fig. 5.22, using A572 steel with yield stress of 42 ksi and assuming

a.    full lateral support

b.    lateral supports at points A and B only

 

5.15 A built-up simply supported beam consists of a W24x68 and a C15x33.9 as shown in Fig. 5.23. The beam has a span of 30 ft and full support. Using A36 steel (Fy = 36 ksi), find the maximum uniformly distributed load this beam can carry.


 


5.16 The cross section of the cantilever beam of Fig. 5.24 is shown in Fig. 5.25. Find the maximum load-carrying capacity of this beam (qmax), using A36 steel (Fy = 36 ksi) and assuming

a.    full lateral support

b.    lateral supports at points A and B only

 


5.17 A simple beam with a span of 15 ft is subjected to two concentrated vertical loads, as shown in Fig. 5.26, and a uniformly distributed horizontal load of 0.5 K/ft. Find the lightest W12 section for the beam, using A36 steel (Fy = 36 ksi) and assuming

a.    full lateral support

b.    lateral supports at points A, B, C, and D only


 


5.18 Solve the problem 5.17, substituting the uniformly distributed horizontal load by a concentrated horizontal load of magnitude 7.5 K applied at the middle point of the span. Assume that all the loads pass through the centroid of the section and thus produce no torsional effect.

 

5.19 In example 2 of this chapter, suppose a cover-plated W14 x 30 is used for the beam. What should be the size of the cover plates for the beam to carry the specified load? Assume that the cover plates are welded properly to the beam flanges.

 

5.20 Find the lightest W18 for Example 3 of this chapter.

 

 

 
Hojjat Adeli, Professor
Department of Civil & Environmental Engineering and Geodetic Science
The Ohio State University 
409 Hitchcock Hall, 2070 Neil Avenue, Columbus OH 43210