Abstract—In this study, static and dynamic responses of a typical reinforced concrete solid slab, designed to British Standard (BS 8110: 1997) and under self and live loadings for dance halls are reported. Linear perturbation analysis using finite element method was employed for modal, impulse loading and frequency response analyses of the slab under the aforementioned loading condition. Results from the static and dynamic analyses, comprising of the slab fundamental frequencies and mode shapes, dynamic amplification factor, maximum deflection, stress distributions among other valuable outcomes are presented and discussed. These were gauged with the limiting provisions in the design code with a view of justifying valid optimization objective function for the structure that can ensure both adequate strength and economical section for large clear span slabs. This is necessary owing to the continued increase in cost of erecting building structures and the squeeze on public finance globally. Keywords—Economical design, Finite element method, Modal dynamics, Reinforced concrete, Slab. I. INTRODUCTION TEEL rods embedded in concrete, also known as Reinforced Concrete (RC) have been widely reported to have good compressive and tensile strengths owing to the complimentary strength contribution of the two constituents. This excellent property of reinforced concrete, among others, has for many years been reason for its widely used in construction of structural elements. Tensile strength of plain concrete is reported to be only about 10 per cent of its compressive strength [1]; hence in design of RC structures the embedded reinforcements are generally assumed to carry tensile forces which are transferred to it by bond between interfaces of the two materials. Research to improve concrete durability [2], strength and cost [3], largely carried out by partial replacement of the traditional constituents materials with cheaper alternatives have yielded some interesting outcomes. Considering however, the usual high volume of concrete used in buildings, the cost of producing concrete can still be said to be high. Thus, further research dwelling on optimum utilization of concrete in buildings and other structures is essential and hence this study. Designs of RC structural elements are mostly based on either national or international standards (codes), which are often put together to ensure provision of sections with Dr Aaron Aboshio is a civil structural engineering lecturer at Bayero University, Kano-Nigeria, PMB 3011 (phone: +2347037962610; e-mail: aaboshio.civ@ buk.edu.ng). Prof. Jianqioa Ye is a professor of Structural mechanics at Lancaster University, UK (e-mail: j.ye2@lancaster.ac.uk). adequate strength to resist both self and live loads during the expected service life of the structure. Limits for RC materials as well as its response to load are normally set; chief among the limiting factors especially for flexural elements is the maximum allowable deflection- a provision that ensures RC section of adequate stiffness to prevent both structural damage and serviceability concerns. Various codes have different approach to this: Eurocode (EC 2) and BS 8110 set span-to-depth ratio for continues two-way solid slabs at 26, which can be modified upwards dependent on the reinforcement density in the concrete [4]. Other codes require detailed estimation of deflections as against the empirical limits of the span-depth ratios. In design practice, using the BS 8110 and allied codes, the span-depth ratio is the bases for sizing of RC slabs and beams. This tradition, though very convenient in practical design of residential and commercial buildings is however, tantamount to having a generous sections that undermines the essence of having an economic section/design. This paper thus, considers analysis of a commonly employed two-way solid slab for dance halls or event centres under self and dynamic live loading allowance of 5kN/m 2 as stipulated in BS 8110. Static and dynamic analyses of the structural element under wide conditions were carried out using Abaqus commercial finite element code, employing the general static and linear perturbation analysis respectively. This is with a view to estimate static instantaneous maximum deflection of the slab as well as modal dynamic deflections over a wide range of forcing function frequencies. Results from the aforementioned analysis were compared with the allowable limits to justify or otherwise state the effect of application of the span-depth ratio in design of slabs. II. GOVERNING EQUATIONS Structures under static loading can be described by the equation of equilibrium (1) which can be linear or non-linear depending on the structural material and the loading regime. F KU = (1) Under dynamic loading condition however, this is described using the equation of motion given by: ) (t F KU U C U M = + +    (2) where in both cases, K is the stiffness matrix, U is the displacement vector, (KU-internal force), M is the mass matrix and C is the viscous damping matrix of the structure. Reinforced Concrete Slab under Static and Dynamic Loadings Aaron Aboshio, Jianqioa Ye S World Academy of Science, Engineering and Technology International Journal of Civil and Environmental Engineering Vol:9, No:12, 2015 1511 International Scholarly and Scientific Research & Innovation 9(12) 2015 ISNI:0000000091950263 Open Science Index, Civil and Environmental Engineering Vol:9, No:12, 2015 publications.waset.org/10002901/pdf