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It can be seen from the stress distribution of a loaded beam that the greatest stress occurs at the top and bottom extrem ities of the beam.
This led to the improvement on a rectangular section by introducing the l-section in which the large flanges were situated at a distance from the neutral axis. In effect, the flanges carried the bending in the form of tension stress in one flange and compression stress in the other, while the shear was carried by the web.
For these situations where bending is high but shear is low, for example in roof design, material can be saved by rising a framework design. A truss is a pinpointed framework.
A truss concentrates the maximum amount of materials as far away as possible from the neutral axis. With the resulting greater moment arm (h), much larger moments can be resisted.
Resistance of a truss at a section is provided by:
M = C x h = T x h, where C = T in parallel cords and:
C = compression in the top chord of the truss.
T = tension in bottom chord of a simply supported truss.
h = vertical height of truss section.
If either C, T or h can be increased, then the truss will be capable of resisting heavier loads. The value of h can be increased by making a deeper truss.
Allowable C or T stresses can be increased by choosing a larger cross section for the chords of the truss, or by changing to a stronger material.
A framework or truss can be considered as a beam with the major part of the web removed. This is possible where bending stresses are more significant than shear stresses. The simple beam has a constant section along its length, yet the bending and shear stresses vary. The truss, made up of a number of simple members, can be fabricated to take into account this change in stress along its length.
The pitched-roof truss is the best example of this, although the original shape was probably designed to shed rain water. Roof trusses consist of sloping rafters which meet at the ridge, a main tie connecting the feet of the rafters, and internal bracing members. They are used to support a roof covering in conjunction with purling, which are members laid longitudinally across the rafters, the roof covering being attached to the purling. The arrangement of internal bracing depends on the span. Rafters are normally divided into equal lengths, and ideally, the purlins are supported at the joints, so that the rafters are only subjected to axial forces. This is not always practicable, since purlin spacing is dependent on the type of roof covering. When the purlins are not supported at the panel joints, the rafter members must be designed for bending as well as axial force. See Figure 4.5.
The internal bracing members of a truss should be triangulated and, as far as possible, be arranged so that long members are in tension and compression members are short to avoid buckling problems.
The outlines in Figure 4.6 give typical forms for various spans. The thick lines indicate struts.
Figure 4.5 Truss components.
The lattice girder, also called a truss, is a plane frame of open web construction, usually having parallel chords or booms at top and bottom. There are two main types, the N (or Pratt) girder and the Warren girder. They are very useful in long-span construction, in which their small depth-to-span ratio, generally about 1/10 to 1/14, gives them a distinct advantage over roof trusses.
Steel and timber trusses are usually designed assuming pin-jointed members. In practice, timber trusses are assembled with bolts, nails or special connectors, and steel trusses are bolted, riveted or welded. Although these rigid joints impose secondary stresses, it is seldom necessary to consider them in the design procedure. The following steps should be considered when designing a truss:
1 Select general layout of truss members and truss spacing.
2 Estimate external loads to be applied including self weight of truss, purlins and roof covering, together with wind loads.
3 Determine critical (worst combinations) loading. It is usual to consider dead loads alone, and then dead and imposed loads combined.
4 Analyze framework to find forces in all members.
5 Select material and section to produce in each member a stress value which does not exceed the permissible value. Particular care must be taken with compression members (struts), or members normally in tension but subject to stress reversal due to wind uplift.
Unless there are particular constructional requirements, roof trusses should, as far as possible, be spaced to achieve a minimum of weight and economy of materials used in the total roof structure. As the distance between trusses is increased, the weight of the purlins tends to increase more rapidly than that of the trusses. For spans up to about 20m, the spacing of steel trusses is likely to be about 4m, and in the case of timber, 2m.
The pitch, or slope, of a roof depends on locality, imposed loading and type of covering. Heavy rainfall may require steep slopes for rapid drainage; a slope of 22° is common for corrugated steel and asbestos roofing sheets. Manufacturers of roofing material usually make recommendations regarding suitable slopes and fixings.
Figure 4.6 Types of trusses.
To enable the designer to determine the maximum design load for each member, the member forces can be evaluated either by calculation or graphical means, and the results tabulated as shown:
|Dead + Imposed
A simplified approach can he used if the intention is to use a common section throughout. Once the layout has been chosen, the member which will carry the maximum load can be established. An understanding of the problems of instability of compression members will lead the designer to concentrate on the top chord or rafter members. A force diagram or method of sections can then be used to determine the load on these members, and the necessary size.
A farm building comprised of block walls carries steel roof trusses over a span of 8m. Roofing sheets determine the purlin spacings.
Assume a force analysis shows maximum rafter forces of approximately 50kN in compression (D + 1) and 30kN in tension (D + W), outer main tie member 50kN tension (D + 1) and 30kN compression (D + W). A reversal of forces due to the uplift action of wind will cause the outer main tie member to have 50kN of tension and 30kN of compression.
Consulting a structural engineering handbook reveals that a steel angle with a section of 65mm x 50mm x 6mm and an effective length of 1.8m can safely carry 29kN in compression.
Rafter: Using two angles back-to-back will be satisfactory, since distance between restraints is only 1.38m. (Note angles must be battened together along the length of the rafter).
Main Tie: The 65mm x 50mm x 6mm section can carry the required tensile force. Although its length is a little greater than 1.8m, the compressive load brought about by the uplift of the wind is safe since the design codes allow a greater slenderness ratio for intermittent loads such as wind.
Finished Design: Note the use of a sole plate to safely distribute the load to the blockwork wall, so that the bearing stress of the blocks is not exceeded. See Figure 4.7.
Figure 4.7 Finished design of roof truss.
Apart from the roof truss, there are a number of other structural frames commonly used in farm building construction. They include portal frames, pole barns, and postand-beam frames.
A single-bay portal frame consists of a horizontal beam or pitched rafters joined rigidly to vertical stanchions on either side to form a continuous plane frame. For the purposes of design, portal frames can be classified into three types: fixed base, pinned base (2 pins), pinned base and ridge (3 pins).
The rigid joints and fixed bases have to withstand bending moments and all bases are subjected to horizontal as well as vertical reactions. Hence foundation design requires special attention. The externally applied loads cause bending moments, shear forces and axial forces in the frame.
Portal frames are statically indeterminate structures and the complexity of the analysis precludes coverage here. However, the results of such calculations for a number of standard cases of loading are tabulated in handbooks. Using these and the principle of superposition, the designer can determine the structural section required for the frame. Determining the maximum values of the bending moment, shear force and axial force acting anywhere in the frame; allows the selection of an adequate section for use throughout the frame. Care must be exercised to ensure that all joints and connections are adequate.
Portal frames may be made of steel, reinforced concrete or timber. With wider spans the structural components become massive if timber or reinforced concrete is used. Hence, steel frames are most common for spans over 20m. At the eaves, where maximum bending moments occur, the section used will need a greater depth than at other points in the frame.
Figure 4.8 Portal or rigid frame.
Pole barns are usually built with a relatively simple foundation, deeper than usual, and backfilled with rammed earth. Pole barns are braced between columns and rafters in each direction. The braces serve to reduce the effective length of compression members and the effective span of rafters and other beam members. This leads to a structure which is simple to analyze and design, and can be a lowcost form of construction.
A shed type building is a simple construction consisting of beams (horizontal or sloping), supported at their ends on walls or posts. There may be one or more intermediate supports depending on building width. Purlins running longitudinally support the roof covering. As the principle members are simple or continuous beams, (very often timber of rectangular section), the stress analysis aspect of the design is straight forward. When the beam is supported by timber posts, the post design is not difficult since the load is assumed to be axial. Like the poles in the pole barn, the foundation can consist of a simple pad of concrete beneath the post, or the base of the post can be set into concrete.
Designing of a building using block walls, timber posts and rafters
It is assumed that the knee braces reduce the effective span of the rafters between the central wall and the timber posts.
Self-weights and service load have been estimated. Continuity over post and brace have been disregarded. This provides a simple but safe member.
Self-weights and service load
Max. shear force 5kN
Max. bending moment 3120kNmm Try 2 rafters 38 x 200 (back to back)
Max. sheer stress = 3Q / 2bd = 3 / 2 x (5000 / 76 x 200) = 0.49N/mm²
Max. bending stress = Mi / I = M / Z = (3120 x 103 x 6) / 76 x 2002 = 6.2N/mm²
Tables of allowables stresses indicate that most hardwoods, but not all softwoods are adequate.
Load transferred to outer wall by rafters is a little over 3kN. Assuming the strength of the blocks is at least 2.8N/mm², the area required:
3000 / 3.8 = 1072mm², since rafter underside is 76mm the minimum interface across wall is 1072 / 76 = 14mm
Hence, there is no problem of load transfer to wall.
Assume posts 100 x 100mm and 2.5m long, l / b = 25 and table 4.5 gives Kl = 0.3
With s c = 5.2N/mm² allowable for design, 0.38 x 5.2N/mm² x 1002 @ 20kN The load is safe.
The methods used to join members include lapped and butt connectores. Bolt and connector joints, nailed joints and glued joints and sometimes a combination of two are examples of lapped connections. Butt connections require the use of plates or gussets. In all cases the joints should be designed by calculating the shear forces that will occur in the members.
If two members overlap the joint is called a single-lap joint. If one is lapped by two other members, i.e., sandwiched between them, it is called a double-lap joint.
With a single lap the joint is under eccentric loading. For small-span trusses carrying light loads, this is not significant, but when the joints carry large loads eccentricity should be avoided by the use of double-lap joints. Double members are also used to obtain a satisfactory arrangement of members in the truss as a whole.
Sandwich construction enables the necessary sectional area of a member to be obtained by the use of relatively thin timbers, any double members in compression being blocked apart and fixed in position to provide the necessary stiffness.
The use of gussets permits members to butt against each other in the same plane, avoids eccentric loading on the joints and provides, where necessary, greater joining area than is possible with lapped members. This is often an important factor in nailed and glued joints. Arrangement of members on a single centre line is usually possible with gussets.
When full-length timber is not available for a member, a butt joint with cover plates can be used to join two pieces together. This should be avoided, if possible, for the top members (rafters) of a truss and positioned near mid-span for the bottom member (main tie).
Figure 4.9 Butt Joints.
Bolt and Connector Joints
Simple bolted joints should only be used for lightly loaded joints, since the bearing area at the hole (hole diameter times member thickness) and the relatively low bearing stress allowed for the timber compared with that of the steel bolt, may cause the timber hole to elongate and fail.
Timber connectors are metal rings or toothed plates used to increase the efficiency of bolted joints. They are embedded half into each of the adjacent members and transmit load from one to the other. The type most commonly used for light structures is the toothed-plate connector, a mild-steel plate cut and stamped to form triangular teeth projecting on each side that embed in the surfaces of the members up on tightening the bolt which passes through the joint. The double-sided toothed connector transmits the load and the bolt is assumed to take no load.
Glues made from synthetic resins produce the most efficient form of joint, as strong as or even stronger than the timber
joined, and many are immune to attack by dampness and decay. With this type of joint all contact surfaces must be planed smooth, and the necessary pressure provided during setting of the glue. Bolts or nails which act as cramps are often used and left in place.
The members may be glued directly to each other using lapped joints or single-thickness construction may be used by the adoption of gussets. As with nailed joints, lapped members may not provide sufficient gluing area and gussets must then be used to provide the extra area.
Glued joints are more often used when trusses are prefabricated because control over temperature, joint fit and clamping pressure is essential. For home use glue is of the used together with nail joints.
Figure 4.10 Double sided Toothed Plate connector.
Joining by nails is the least efficient of the three methods referred to, but is an inexpensive and simple method, and can be improved upon by using glue in combination with the nails.
When trusses are pre-fabricated in factories, nailing plates are often used to connect the member. These fasteners come in two types:
1 A thin-gauge plate called a pierced plate fastener, which has holes punched regularly over its surface to receive nails. The pierced plate can also be used for on-site fabrication.
2 A heavier plate with teeth punched from the plate and bent up 90 degrees, called a toothed-plate fastener, or connector. The type, in which the teeth are an integral part of the plate, must be driven in by a hydraulic press or roller.
Figure 4.11 Truss gussets.
Figure 4.12 Nailing plates for truss construction.
In order to permit the development of the full load at each nail, and to avoid splitting of the wood, minimum spacings between nails and distances from the edges and ends of the member are necessary.
Nailing patterns for use on timber structures are usually available locally. They are dependent on the quality and type of nails and timber used, and are based on the safe lateral nail load.
The Housing Research and Development Unit of the University of Nairobi investigated timber nailed joints made with spacings in accordance with the continental standard for timber joints, which proved to be satisfactory. The main principles are given in table 4.9 and 4.10.
Table 4.9 Minimum nailing spaces
Connections in Steel Structures
Connections may be bolted, riveted or welded. The principal design considerations are shear, tension and compression, and the calculations are relatively straightforward for the types of design covered.
d: Diameter of nail mm.
r0: Distance from extreme row of nails to unloaded edge of member.
d1: Distance between two nails in nailing area, measured perpendicular to axis of member.
d11: Distance between two nails measured parallel to axis of member.
rb: Distance from extreme row of nails to loaded edge of member.
e0: Distance from the nearest row of nails to the unloaded end of member.
eb: Distance from the nearest row of nails to the loaded end of member.
Figure 4.13 Connections for steel frames.
Stability problems in a building are due mainly to horizontal loads such as those resulting from wind pressure, storage of granular products against walls, soil pressure against foundations, and sometimes earthquakes.
Overturning of foundation walls and foundation piers and pads is counteracted by the width of the footing and the weight of the structure. Only in special cases will it be necessary to give extra support in the form of buttresses.
Overturning of external walls is counteracted by the support of perpendicular walls and partitions. Note however, that not all types of walls, for example framed walls, are adequately rigid along their length without diagonal bracing. If supporting walls are widely spaced and/ or the horizontal loads are large, extra support can be supplied by the construction of piers, columns or buttresses. See Chapter 5.
Diagonal bracing is used to make framed walls and structures stiff. Long braces should preferably transfer the load with a tensile stress to avoid buckling. Braces are usually supplied in pairs, i.e., on both diagonals, so that one will always be in tension independent of wind direction.
If the framed wall is covered with a sheet material, like plywood, chipboard or metal sheets, the lateral forces on the frame can be counteracted by shear in the sheets. This design requires that the sheets to be securely fixed to the frame, both horizontally and vertically. The sheets must also be strong enough to resist buckling or failure through shear.
Masonry and concrete walls which are stiff and capable of resisting lateral wind loading are called shear walls.
Portal or rigid frame buildings are normally stable laterally, when the wind pressure acts on the long sides. However, when the wind loads occur at the gable ends, the frames may need extra support from longitudinal bracing. Tension rods are frequently used.
Figure 4.14 Bracing for portal frame.
Post-and-beam or shed-frame buildings will, in most cases, require wind bracing, both along and across the building since there are no rigid connections at the top of the wall to transfer loads across and along the building. The same applies to buildings employing roof trusses. End bracing should be installed.
Walls with long spans between the supporting crosswalls, partitions or buttresses tend to bend inwards due to wind load or outwards if bulk grain or other produce is stored against the wall. At the bottom of the wall this tendency is counteracted by the rigidity of the foundation (designed not to slide) and the support of a floor structure. The top of the wall is given stability by the support of the ceiling or roof structure or a specially designed wall beam which is securely anchored to the wall.
The designer must consider the ability of the building to withstand horizontal loading from any and all directions, without unacceptable deformation.
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