SLX 09: prestressed bar

Description

Material		Modulus of elasticity	$E =210 000N/mm^2$
		Poisson’s ratio	$\nu= 0.25$
		Thermal delation	$\alfa= 0.000 01 / ^{\circ}C$
Geometry	Cross-section	bar A-D-F-B: Area	$A = 15 160 mm^2$
		bar A-D-F-B: Moment of intertia	$I = 217 400 000 mm^4$
		bars DC & EF: Area	$A = 3 480 mm^2$
		bars DC & EF: Moment of intertia	$I = 2 000 000 mm^4$
		bar A-C-E-B: Area	$A = 4 500 mm^4$
		bar A-C-E-B: Moment of intertia	$I = 2 000 000 mm^4$
		Factor for shear for all bars	$\lambda = 2.50$
	Boundary conditions	Point A	Simple support
		Point B	Roller support
		bars DC & EF	Hinged at both ends
Loads		on bar A-D-F-B	$q = 50 kN/m$
Loads		on bar CE	shortening of 6.52mm

Note: the shortening is modelled as a temperature load in Diamonds. A shortening of 6,52mm corresponds to a temperature decrease of 163°C.

$\Delta T=\frac{\Delta L}{\alpha \cdot L}=\frac{-6.52mm}{0,00001 /^{\circ}C \cdot 4000mm}=-163^{\circ}C$

Results

Deformation $\delta_y$ in Diamonds

Location	Which result	Independent reference	Diamonds	Difference
bar CE	Tensile force $N$	585,584kN	584,549kN	-0,18%
H	Bending moment $M_y$	49,249kNm	49,249kNm	-0%
D	Deformation $\delta_y$	-0,5428mm	-0.5418mm	-0,18%

References

Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLL 13: poutre sous-tendue.

Tested in Diamonds 2023r01.

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