• Bolt force due to moment is proportional to the distance from the bolt to the centroid of the bolt group (Fig. 9(a)).

• The axial and shear force is subpided equally between the number of bolts (Fig. 9(b)). The design calculations shows that six, M20 Grade 8.8 high strength bolts are adequate for the eaves and apex joints of the portal frames. Grade 8.8 bolts have a minimum tensile stress fu=800 MPa.  2a result of the applied moment Mu, Fa is the axial force, Fs is the shear force, Fx is the bolt force in x-direction,

and Fy is the bolt force in y-direction. The forces for bolts 1 and 4 are determined from the same expressions and a bolt angle of α. Bolts 3 and 6 are lightly loaded (Fig. 5) and are therefore not critical. The moments due to the ultimate loads (Mux) at the eaves joints and the moment of resistance of the joints (Mrj) of the three frames are presented in Table 8. Parameter r1 and r2 are distances from bolt 1 and bolt 2 to the centroid of the group of bolts respectively. Mrj is evaluated, based on the bearing resistance of the plate (Br), which in all cases is much less than the shearing resistance of the bolts. Bearing capacity (resistance) of the connections is established from the following equation:

Br=φatfu≤φCdtfu (9)

where, φ is the bearing resistance factor (0.67), t is the thickness of the channel, d is the diameter of bolt, fu is the minimum tensile strength of the channel and a is the distance from centre of hole to the edge towards which the force is directed. Based on the design recommendation of Kemp (2001), a coefficient C of 1.8 for a standard washer under the nut and bolt head is used in bearing resistance calculations. The coefficient represents a lower bound value rather than the mean value for interpreting test results. This factor depends on the ratio of bolt

diameter to member thickness. The design calculations in the code shows that six, M20 Grade 8.8 high strength bolts are adequate for the eaves and apex joints of the

portal frames (Table 8).

8.2. Base connection

The base connection in Fig. 2 is designed for the case of axial force, and a proportion of the eaves moment assumed to be 50% of the moment of a fixed base. This represents a moment that is halfway between a fixed and a pinned condition. The tensile force of 13.85 kN is much smaller than the tensile resistance of a holding-down bolt

(67.85 kN). The holding down bolt provides the tensile resistance required to maintain equilibrium. The 150×90 ×10 mm angle is connected to the foundation using an M20 Grade 8.8 bolt and to the column using 2M20 Grade 8.8 bolts. Tests have shown this angle to be capable of transferring the load from the column into the foundation

(Dundu and Kemp, 2008; Dundu and Maphosa, 2010). 9. Serviceability Requirements of Portal Frames

It is imperative that an analysis at the serviceability limit state be carried out to check deflections at both eaves and apex. Although the service loads are notably

smaller than the ultimate loads on a structure, the magnitude of deflections of a structure under service loads may be as important a design consideration as the

strength of a structure under ultimate loads. The check is required, not only to ascertain whether deflections are excessive, but also as a check to ensure that the deflections and accompanying frame movements can be accommodated by the building envelope without undue cracking of any brick or tearing of metal cladding sheets at fixed positions. Since the use of cold-formed steel portal frames is limited

to light industrial buildings without gantry cranes, there are only three main considerations for deflection limits;

(1) Horizontal deflection at the eaves should not cause damage to the cladding or brickwork.论文网

(2) The difference in horizontal deflection at the eaves between the end frame and the adjacent internal frame is often a problem as the end frame not only carries half the load of the internal frames but is also much stiffer as a result of the sheeting and internal columns within the end frame. This is exacerbated by the fact that the same section sizes and details used for the internal frames are often used for the end frames. Differential horizontal deflection at the eaves should not be excessive, otherwise significant stressed skin action will develop. Fixings may