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SUMMARYA robust two-field hexahedral element capable of handling plate/shell, beam and nearly incompressible material analyses without locking are presented. Starting with the assumed stress element of Pian and Tong,7 parasitic strain components leading to locking in plate, shell and beam analyses are first identified. Locking can be alleviated by scaling down selectively the parasitic strain components in the leverage matrix. Unfortunately, the element then fails the patch test. However, patch test correction and reduction in computation can be achieved by the recently proposed adrnissihle matrix formulation. The resulting element is lock-free and very efficient. All matrices involved in constructing the stiffness matrix can be derived explicitly. The accuracy of the element is tested by popular bench-mark problems. INTRODUCTlONHybrid elements, originated by Pian' in the sixties and subjected to continuous development since then, are probably one of the most accurate class of finite elements. In their formulation, either stress or strain fields are assumed (Hellinger-Reissner functional), or both fields are assumed (Hu-Washizu functional) in addition to the displacement field. For analysis of plates and shells, use of assumed strain fields is more popular than assumed stress fields. Linear variation of strain is often assumed over the thickness of plate or shell, similar assumption is not realistic for stress in non-linear material.' Nevertheless, hybrid stress elements often offer more accuracy than hybrid strain elements, because equilibrium can be satisfied more readily by selection of stress modes rather than strain modes.In the recent years, some investigators have developed tailor-made solid elements for thinplate/shell a n a l y~i s .~,~ The chief advantage of using a solid element for thin-platelshell analysis is that rotational d.0.f. are not required to dcscribe the kinematics. No special effort would then be necessary in matching the translational and rotational d.0.f. when structures are unavoidably modelled by both solid and plate/shell meshes. Moreover, in large-displacement analysis of shells, the controversial question of how to update the nodal rotations willno more exist (see e.g.Reference 5). It should, however, be mentioned that, when solid elements are used in shells, some of the translational d.0.f. normal to the shell surface are wasted without contributing to better accuracy since the thin mesh is in an essentially plane stress condition.Designing solid element for thin platelshell analysis is no doubt a very demanding task and the difficulty becomes even more subtle when the element is a low-order one such as the eight-node

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This paper provides an overview of serviceability specifications given by the fib Model Code for Concrete Structures 2010 (fib MC2010 [1]). First, the reasons behind crack control and deflection control are discussed, then specific design rules are provided. Simple rules as well as detailed models are also presented. Numerical examples are provided in order to assist in the application of the design recommendations for crack control and deflection control (reinforced and prestressed concrete elements).Simple rules mean indirect control of cracking or deflections without calculations. Indirect crack control may include limitation of stresses and selection of maximum bar diameter or maximum bar spacing. Indirect deflection control normally means limiting the span‐to‐depth ratio.Detailed models are based on physical and mathematical approaches to cracking and deflections. The design crack width is expressed as the maximum bond transfer length multiplied by the mean strain between cracks. Deflection analysis can be provided by integrating curvatures or by using a simplified or refined method. Vibrations and numerical modelling of cracking are also briefly discussed.

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