PSI - Issue 81

Volodymyr Romaniuk et al. / Procedia Structural Integrity 81 (2026) 276–281

278

(a)

(b)

1 – perforated chords; 2 – tie rod; 3 – spacer; 4 – prestressing mechanism; 5 – suspension.

Fig. 1. Steel prestressed perforated arch: (a) – general view; (b) – half-arch with characteristic cross-sections.

where q – is the external vertical uniformly distributed symmetrical load on the arch; α – is the angle of inclination of the arch half chords to the horizontal; f – is the height of the arch, which is taken from a full-scale experiment and is 2.25 m; f 1 – is the height of spacer placement. Since the structural scheme of the arch is doubly statically indeterminate, the tie rod force can be determined using the force method

(

)

(

) (

)

  

  

(

)

(

)

2

5 8

2 f e f

2 3 3 e e f f + − + +

2

2

3 2

4

6

q f

e f f + +

f

f f

− −

1

1

o

o

o

o

(3)

Р

=

(

) (

) (

)

(

)

 

 

2

2 4 3 3

2

2sin tg

3 2

α α f f −

f e e f f

f f + + − −

e f f + +

1

1

1

o

o

o

By equating the right-hand sides of expressions (1) and (2) and substituting the value calculated by formula (3) into them, we obtain a second-degree equation, one solution of which is the formula for calculating e 0 ( ) 3 3 2 2 6 6 3 3 5 5 4 2 4 2 1 1 1 1 1 1 1 1 1 2 2 1 1 9 15 3 9 180 18 150 195 363 36 24 60 o f f f f f f f f f f f f f f f f f f e f f f f − − + + − + − + − + + = − − (4) The optimal value of the height of spacer placement f 1 is determined from the condition that the total mass of the arch is minimized and, as the results of the study showed, such an optimal value is the placement of the spacer at a height f 1 = 0.685 f as shown in Romaniuk et al. (2008). By substituting this value into formula (4) and performing some mathematical simplifications, the most rational eccentricity of the tie displacement was determined

2.25 19.542 19.542 f =

(5)

0.115m

0 е =

=

Experimental studies of a perforated steel arch with tie rod and spacer with span L = 9 m, rise f = 2.25 m (Fig. 1, a) featuring a rigid flanged ridge node A , support hinge nodes B and C , and spacer fastening nodes D (Romaniuk et al. 2008, Romaniuk et al. 2024a) were conducted in the research laboratory of the Department of Industrial, Civil Construction and Engineering Structures of the National University of Water and Environmental Engineering (Rivne, Ukraine). The calculated symmetrical uniformly distributed load on the arch was 8.35 kN/m. During experimental studies, it was replaced by concentrated equivalent nodal loads of 8.4 kN, applied with a step of 0.9 m. To implement the above purpose and tasks, experimental studies were conducted at different values of tie displacement eccentricity, which was enabled by the design feature of support nodes B and C (Fig. 2). Construction of supports allows it to be placed in five positions along the arch height with a step of 50 mm.