5500 EN2400 Structural Analysis and Design DESIGN SHORT 4 - ANALYSIS AND DESIGN OF A STEEL AND CONCRETE INFILL FRAME The owner of a building complex has planned to infill the space between two existing adjacent buildings with a new multi-bay single storey building and roof garden. The new 30-metre long structure will comprise frames at 5m centres that support a pre-cast concrete roof deck. A cross-section through one of the internal frames is shown in Figure 4.1. The variable load to be supported by the roof deck has been calculated to allow for a garden area and a set of light-weight free-standing structures. You are required to design both an internal concrete frame and a steel frame to support the roof structure and associated loads, assuming that both frames are continuous structures. You should undertake a series of analyses by hand using the stiffness-based matrix method. Details of the analysis cases to be considered are given on page 2 of this design brief. You should NOT undertake a computer analysis of these frames. You are required to provide full calculations and sketches to support your answers. You should assume the following: • The roof deck comprises 250 thick precast concrete units that span between the frames, overlaid with a 50mm mortar screed. The total characteristic permanent load of the units and screed is 5kN/m². • The characteristic variable load is 7.5kN/m². • The beams are pinned at their intersection with the existing buildings. • The existing buildings have structural elements capable of supporting the beam loads at the necessary locations. • The columns are supported by an existing raft foundation located 1000mm below the finished floor level (FFL) of the new structure. • There are pinned supports at the base of the columns. • The beam-column connections should be considered continuous (i.e. moment carrying). FFL 1000 Existing building Concrete or steel structural frame 3500 All dimensions are in mm. Precast floor units and screed 5500 4000 Concrete raft foundation Existing building Figure 4.1. Cross-section through an internal frame EN2400 Structural Analysis and Design DESIGN DATA Concrete frame fcteff=3.5N/mm2, fyk=fywk 500 N/mm², Es=200kN/mm², cover=30mm Pconc= 25 kN/m³, fck= 40 N/mm², Ecm=35kN/mm², Steel frame Psteel 78 kN/m³, Steel S275 (Fe430) ANALYSIS = • The rotational stiffness (M/0) of a pin-ended beam =3EI/L; • The rotational stiffness (M/0) of a fixed-end beam = 4EI/L; • The fixed end moment for a beam built-in at both ends = wL²/12; • The fixed end moment at the built-in (encastré) end of a beam with a pin support at one end and an encastré support at the other end = wL²/8 • You are not expected to redistribute moments. Important: You will only need to solve a 2x2 system of equations with the primary unknowns being the rotations at the two column/beam intersections. Consider the following load cases for both frames; i. ii. iii. iv. V. vi. Ultimate permanent + variable load across the entire length of the continuous beam. Ultimate permanent + variable load on the central span only and the unfactored permanent load on the outer spans. Serviceability permanent + variable load across the entire length of the continuous beam. Serviceability permanent + variable load on the central span only and the unfactored permanent load on the outer spans. Quasi-permanent load across the entire length of the continuous beam. Quasi permanent load on the central span only and the unfactored permanent load on the outer spans. Note: Every group member must undertake the analysis of at least one of these cases independently. You may limit the number of cases considered to the number of members in your group. EN2400 Structural Analysis and Design CONCRETE FRAME DESIGN Beam: • Design the bottom flexural reinforcement for the maximum ultimate sagging moment and the top flexural reinforcement for the maximum ultimate hogging moment. • Design the shear reinforcement for the maximum value of shear at a distance d (effective depth) from a support. • Check crack widths for the maximum serviceability moment (hogging or sagging). Check the deflection, using the L/d criterion, for the most onerous span of the continuous beam. • Consider curtailment of the flexural and shear reinforcement. Columns: • Design the column for the most onerous combination of ultimate axial load and moment. • • Add the nominal eccentricity moment to the ultimate moment from the applied loads and check the minimum moment criterion. Size the column by assuming Lo=0.80L and that the column is 'short'. Specifically, your column should satisfy the condition λim; where lim=40. STEEL FRAME DESIGN Beam: • Design the beam so that it can sustain both (i) the maximum ultimate sagging moment, based on the assumption that the compression flange is fully restrained, and (ii) the maximum ultimate hogging moment, based on the assumption that the compression flange is unrestrained. To determine the effective length of unrestrained parts of the beam you will need to plot the bending moment diagram and find the distance between the points of contraflexure. • Check the shear capacity of the cross-section for the maximum ultimate shear force. You will also need to check the effects of coexistent moment and shear. • Check the deflection for the most onerous span of the continuous beam. Columns: Design the column for the most onerous combination of ultimate axial load and moment. The major axis moment should be obtained by combining the moment due to the applied load with the nominal moment due to the eccentricity of the axial load. In determining λLT, allowance will need to be made for the shape of the bending moment diagram. Submission deadline: start of the design office session: Thursday week 11.