SLS 09: Four-sides simply supported plate under uniform load

Description

Length a =1m. Different ratio’s b/a are tested by changing the length of b in each model.

Open handcalculations

$\delta_y=\frac{\alpha \cdot p \cdot a^{4}}{E \cdot e^3}$

$M_{xx,max}=\beta \cdot p \cdot a^{4}$

$M_{zz,max}=\beta_1 \cdot p \cdot a^{4}$

Deformation $\delta_y$ in Diamonds

Case	Which result	Independent reference	Diamonds	Difference
b=1m	Deformation $\delta_y$	4.43mm	0,163mm	-0.77%
	Bending moment $M_{xx}$	0.479N/m/m	0.4818N/m/m	0.58%
	Bending moment $M_{zz}$	0.479N/m/m	0.4818N/m/m	0.58%
b=2m	Deformation $\delta_y$	11.06mm	10.993mm	-0.61%
	Bending moment $M_{xx}$	0.464N/m/m	0.4697N/m/m	1.23%
	Bending moment $M_{zz}$	1.017/m/m	1.0214N/m/m	0.43%
b=5m	Deformation $\delta_y$	14.1632mm	14.081mm	-0.58%
	Bending moment $M_{xx}$	0.375N/m/m	0.3794N/m/m	1.17%
	Bending moment $M_{zz}$	1.246N/m/m	1.2451N/m/m	-0.07%

Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLS 24: plaque rectangulaire sur appuis simples avec chargement uniforme.
Note: the modulus of elasticity and load imposed in the Afnor-example, felt outside the boundaries of Diamonds. As a work around, both parameters were multiplied by 10 and the results were recalculated accordingly.
Timoshenko, S., & Woinowsky-Krieger, S. (1959). Theory of plates and shells. McGraw-Hill Publishing Company.

Need Support?

Can't find the answer you're looking for? Don't worry we're here to help!