University of Sheffield. Department of Civil Structural Engineering. Member checks - Rafter 44.6

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1 Member checks - Rafter Haunch (UB 457 x 191 x 89) The depth of a haunch is usually made approximately twice depth of the basic rafter sections, as it is the normal practice to use a UB cutting of the same serial size as that of the rafter section for the haunch, which is welded to the underside of the basic rafter (UB 457x191x 89). Therefore it is assumed that the haunch has an overall depth at connection is 0.90 m. EN : 2005 (E) Section Classification ε = 275/235 =1.08 Web The web can be divided into two, and classified according to stress and geometry of each. actual (d/t w ) = web 1 ( bending ) ε Class 1 web 2 ( Compressive) ε Class 2 Figure 20 Haunch region cross section classification (King, Technical Report P164) Flanges ( Axial Compressive actual (c/t f )=... Thus the haunch section is a class ε Class1

2 Haunch Stability Supporting notes section 13.1 & 13.3 First, check the stability of the haunched portion of the rafter ( from eaves connection to the haunch/ rafter intersection) as this represents one of the most highly stressed lengths, and with its outstand flange (inner) in compression, this part of the rafter is the region most likely to fail due to instability. As it has already decided to stay the inside corner of the column/haunch intersection (column hinge position), assume that the haunch/rafter intersection is also effectively torsionally restrained be diagonal braces, giving an effective length of 3m as indicated in Fig below. Figure 21 Member stability haunch rafter region (Plum, 1996)

3 Member checks Haunch 36 EN : 2005 (E) clause BB (3)B It would appear that clause BB (3)B is the most appropriate creation to check the stability of the haunched portion, as there is three flanged haunch, so the distance between rotational restraint should be limited to Where: L k is length limit specified where lateral torsional buckling effects can be ignored where the length L of the segment of a member between restraint section at a plastic hinge location and adjacent torsional restraint. L k.. L k... = 3738 mm L k = 3.738m EN : 2005 (E) section BB supporting notes section Appendix B c is the taper factor (shape factor) which accounts for the haunching of the restraint length (BB.3.3.3) 1 1 = 1.15

4 37 Figure 22 Dimensions defining taper factor (BS EN :2005) Is the modification factor for non-linear moment gradient (BB.3.3.2). The plastic moduli are determined for five cross-sections indicated on the figure below, the actual cross-section considered are taken as being normal to the axis of the basic rafter (unhaunched member). The plastic moduli together with the relevant information regarding the evaluation of the ratios N i /M i are given in the following table. The worst stress condition at the hunch/rafter intersection (location 5) is taken.

5 Member checks Haunch 38 Figure 23 Member stability haunch region (Plum, 1996) Position on haunch (FIG ) Distance from the eaves (m) Depth of bottom web (mm) Factored moment (M y,ed ) (KNm) Factored axial force (N Ed ) (KN) Moment capacity (KNm) Plastic modulus (cm 3 ) Ratio (N/M) a Value for (R) calculation (mm) R Value Table 2 Member forces at locations indicated in figure 18

6 39 The modification factor is determined by the form; supporting notes section Appendix A in which R 1 to R 5 are the values of R according to equation below at the ends, quarter points and mid-length ( R values at positions 1 to 5 indicated in Table 2) In addition, only positive values of ( ) should be included where, - R E is the greater of R 1 and R 5 - R s is the maximum value of R anywhere ( R 1 to R 5 ) -,, Where (a) is the distance between the centroid of the member and the centroid of restraining members (such as purlins restraining rafter). Here for simplicity a conservative value of (a) is found by conservative method of ignoring the middle flange as shown if figure (19). Figure 24 Simplification for distance between centriod of rafter and purlin sections

7 Thus this portion of the rafter is stable over the assumed restrained length of 3 m (haunch length), as L s is around 3m. If the value was found to be less than the haunch length then a torsion restraint should be provided in the haunch region as shown below supporting notes section Cross section resistance Shear force effects of Plastic moment resistance The shear in the rafter has been checked above, showing that V Ed < 0.5 V pl,rd. In the haunch, the shear area A v increases more than the applied shear V Ed, so the shear force has no effect on the plastic moment capacity of the haunch.

8 Axial force effects of Plastic moment resistance, supporting notes section 12.4 The tables provided below gives the axial and moment resistances of the haunch section at points 1to 5 shown in figures 18. A series of checks is carried out to determine whether the cross-sectional moment resistance M N,Rd is reduced by coexistence of axial force. Position Distance (mm) N Ed (KN) A (mm 2 ) N pl,rd (KN) A web (mm 2 ) (A web, f y )/y mo (KN) N pl,rd = A f y / y mo and f y =275N/mm 2 Table 3 Axial force at positions indicated in figure 18 for haunch Position Distance (mm) M Ed (KNm) 0.5 A web f y /y mo Is N Ed > 0.25 N pl,rd Does Axial force affect plastic bending resistance No No No No No No No No No No No No No No No Table 4 Checking the significance of axial force on plastic moment of resistance Therefore, the effect of shear and axial on the plastic moment resistance of the column sections can be neglected according to EC3 EN : 2005.

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