### Steel Structures - Plastic Theory

1. Pick the wrong statement

(a) shape factor is ratio of plastic moment and yield moment

(b) load factor is ratio of ultimate collapse load and working load

(c) shape factor depends only upon shape of section.

(d) load factor is shape factor divided by factor of safety

2. Which of the following is the load factor

(a) live load/dead load

(b) failure load/working load

(c) total load/dead load

(d) dynamic load/static load (IES 2000)

3. Shape factor for a rectangular section is

(a) 1

(b) 1.5

(c) 2

(d) 2.5

4. Shape factor for diamond section is

(a) 1.0

(b) 1.5

(c) 2.0

(d) 2.5

5. Shape factor for T section is

(a) 1.33

(b) 1.66

(c) 1.74

(d) 1.86

6. Shape factor for a hollow circular section is

(a) 3/π

(b) π/3

(c) 2/π

(d) 4/π

7. In plastic analysis for flexure, which of the following pairs of shape of section and shape factors are correctly matched?

1. I section ⸺1.4

2. Square ⸺ 1.5

3. Rectangle ⸺ 1.5

4. Circle ⸺ 1.7

(a) 1,2, 3

(b) 2, 3, 4

(c) 3, 4

(d) 1, 2 (IES 1994)

8. The shape factor of the section shown in figure is

(a) 139/82

(b) 145/86

(c) 150/91

(d) 160/97 (IES 1998)

9. A thin hollow box section of 400 mm x 600 mm deep (outer dimension) with uniform plate thickness of 10 mm all round is used for a beam. The plastic modulus of section Zp (in 10⁵ mm³) and shape factor will be

(a) 36, 7/6

(b) 36, 6/7

(c) 42, 6/7

(d) 42, 7/6 (IES 1997)

10. For an I-beam, shape factor is 1.12. The factor of safety in bending is 1.5. If the allowable stress is increased by 20% for wind and earthquake loads, then the load factor is

(a) 1.10

(b) 1.25

(c) 1.35

(d) 1.40 (IES 1995)

**Answers**

1. (d) 2. (b) 3. (b) 4. (c) 5. (c)

6. (d) 7. (b) 8. (b) 9. (d) 10. (d)

**Hints**

9. Plastic section modulus is given by ht(b + h/2) = 600 x 10(400 + 600/2) = 42 x 10⁵ mm³

Elastic section modulus is given by ht(b + h/3).

Hence shape factor = (b + h/2) / (b+h/3) = (400 + 300) / (400 + 200) = 7/6

10. F₁ = (Yield stress/allowable stress) = 1.5

F₂ = (Yield stress/1.2 x allowable stress) = (1/1.2) (1.5) = 1.25

Load factor = shape factor x FOS = 1.12 x 1.25 = 1.40

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