Chapter 7 Restrained Beams 7 1 Introduction Statically

Chapter 7 Restrained Beams

7 -1 Introduction • Statically indeterminate problems require relations between the elastic deformations in addition to the equation of static equilibrium. • Three techniques are discussed: (1) Double-integration; (2) Superposition; (3) Area-moment method. 2

7 -2 Redundant Supports in Propped & Restrained Beams Determinate Beam Indeterminate Beam 3

Both are indeterminate beams 4

7 -3 Application of Double-Integration & Superposition Methods Deflection, Slope & Curvature (see Sec. 6 -2 pg. 183) Moment & Curvature positive negative (see Sec. 5 -2 pg. 135) Equation of Elastic Curve of Beam 5

ตวอยาง (Double Integration) RA Boundary conditions แกสมการทงสอง จะได 7

Table 7 -1 Slope & Deflection at Free End 8

ตวอยาง (Superposition) Boundary conditions 9

Ans 10

ตวอยาง 701. Solve for the reactive elements of the propped beam in Fig. 7 -3 a by two methods (1) the method of superposition, considering RA as redundant support; (2) the doubleintegration method. Superposition Method 400 N A B C = Fig. (7 -3 a) (Fig. II) 11

Fig. I A C From Table 7 -1 12

Fig. II A B C From Table 7 -1 13

A Fig. 7 -3 a = Fig. I + Fig. II Ans 14

Fig. 0 = Fig. I + Fig. II From Table 7 -1 Ans 15

Ans 16

ตวอยาง A B Fig. 0 A Fig. I จากตาราง 6 -2 P B A MB B Fig. II Fig. 0 = Fig. I + Fig. II Ans 25

ตวอยาง Fig. 0 = Fig. I + Fig. II Fig. 0 A B 6, 000 lb A Fig. I 9, 000 lb MA MB B Fig. II จากตาราง 6 -2 Ans 26

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