3 - Tension Members PDF

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PRINCIPLES OFSTRUCTURALSTEEL DESIGN1 INTRODUCTIONStructural design involves creation of framework to support a structure and determination of section properties of its individual elements. Architects design how the structure “looks like” while structural engineers design the structure to hold the lo...

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STEEL

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PRINCIPLES OF

STRUCTURAL STEEL DESIGN

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INTRODUCTION Structural design involves creation of framework to support a structure and determination of section properties of its individual elements. Architects design how the structure “looks like” while structural engineers design the structure to hold the loads under the architectural constraints. They, however, must work hand in hand and in coordination to finish the project efficiently and economically. An economical approach to structural design requires provision of least amount of materials producing adequate strength and to be constructed in simple and easy way to reduce labor cost. 1.1 STRUCTURAL DESIGN PROCESS:

CONCEPTUAL DESIGN - It starts with selection of structural system (Bearing wall, Building Frame, Moment Resisting Frame, Dual System, Cantilevered Column). Then, location and formation of the system elements are defined.

STRUCTURAL ANALYIS - all the loads that act on the structre are defined, the framing is idealized and analysis is perfomed to calculate the internal forces (axial force, shear force, bending moment, torsion) of each element based on different combinations of loads and initial sizes of members.

PRELIMINARY DESIGN - based on analysis, each elelment is designed (in concrete design: amount of reinforcement is calculated, in steel design: sectional strengths are checked vs required strength) based on code provisions

MODIFICATIONS - design refinements are done (adjustment of sizes, selecton of new section properties, modification of layout etc.) and reanalysis is performed until results are satisfactory

DRAFTING - structural plans with fully detailed design drawings are created to aid the construction process

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BASIC TYPES OF STRUCTURES 1.2.1

TRUSSES – consist of slender elements, usually arranged in triangular fashion with top chords, bottom chords, webs and struts. External forces are considered to act only at the nodes that results in internal forces in each member to be axial tensile or compressive only.

1.2.2

FRAMES – used in buildings and are composed of beams (horizontal members or inclined) and columns (vertical members) that are either pin or fixed connected. The loading on a frame causes bending, axial stresses and shear stresses in its members. The strength of such a frame is derived from the moment interactions between the beams and the columns at the rigid or semirigid joints. PORTAL FRAME – single storey, single bay or multi-bay frames with pitched or flat roof

Single Bay, Pitched Roof Portal Frame

Single Bay, Flat Roof Portal Frame

Two-Bay, Pitched Roof Portal Frame

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MOMENT RESISTING FRAME (RIGID FRAME) - three-dimensional frame composed of columns and beams rigidly connected to resist gravity and lateral loads by action of flexure

BRACED FRAME – composed of beams and columns that are “pin” connected to resist gravity loads but with bracing to resist lateral loads.

1.3 LOADS 1.3.1

GRAVITY LOADS (VERTICAL) DEAD LOAD – weight of all permanent elements in structure including self-weight LIVE LOAD – weights of objects temporarily placed on a structure (furniture, equipment, occupants of building), at various positions to produce critical conditions for all elements

1.3.2

LATERAL LOADS WIND LOAD – positive or negative pressure of surfaces of building produced from velocity of air SEISMIC LOAD (EARTHQUAKE) – system if horizontal forces produced by structure’s response to ground motion due to earthquake acting at each level of the building

1.3.3

OTHER MINIMUM LOADS – Fluid pressure, lateral soil pressure, ponding loads, self-straining force

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CODES AND SPECIFICATIONS Structures are designed under the provisions of structural codes and specifications stating requirements and criteria of structural safety, integrity and workability. These codes are guidelines and restrictions and not design procedures implemented in a country, sometimes modified by a city. NATIONAL STRUCTURAL CODE OF THE PHILIPPINES (NSCP) UNIFORM BUILDING CODE (UBC) INTERNATIONAL BUILDING CODE (IBC) AMERICAN CONCRETE INSTITUTE (ACI) AMERICAL INSITUTE FOR STEEL CONSTRUCTION (AISC)

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STRUCTURAL STEEL

Stress-Strain Curve of Mild Steel Tensile strength test is performed to determine the structural properties of steel. A test specimen is subjected to tensile load then stresses and strains are calculated and plotted. Under Hooke’s Law, the stress is directly proportional to the strain up to the proportional limit. The elastic limit is reached after that, followed by the yield point where the stress becomes constant but with increasing strain (yielding or plastic range). The steel then goes strain hardening until it reaches peak stress or ultimate tensile strength, after which the stress decreases with “necking” until it fractures.

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2.1 TYPES OF STEEL 2.1.1

Carbon – mostly iron and carbon, with less than 1% carbon LOW CARBON (MILD) STEEL: contains 0.04%-0.30%, This is one of the largest groups of Carbon Steel. It covers a great diversity of shapes; from Flat Sheet to Structural Beam MEDIUM CARBON STEEL: has a carbon range of 0.31%-0.60%, stronger than mild steel but more difficult to form, weld and cut. HIGH CARBON (TOOL) STEEL: has carbon range of 0.61% to 1.50%, very difficult to cut, bend and weld

2.1.2

Low Alloy – has small amounts of one or more alloying elements such as manganese, silicon, nickel, titanium, copper chromium and aluminum added to increase the strength

2.1.3

Stainless – steel alloy with increased corrosion resistance, with more alloying elements such as chromium at least 11%, nickel or molybdenum. Alloy content is 15-30%

2.2 STRUCTURAL PROPERTIES Different grades of structural steel are identified by the American Society for Testing and Materials (ASTM). Most commonly used structural steel is A36, which is a mild steel containing not more than 0.26% carbon, 0.04$ phosphorous and 0.05% sulfur. Other commonly used are ASTM A572 Grade 50 and ASTM A992. The properties are given in the following table. PROPERTY Modulus of Elasticity Yield Point, min. Tensile Strength, min. Yield to Tensile ratio Elongation in 200 mm

A36 248 MPa 400 MPa to 552 MPa 20%

A572 Gr. 50 200,000 MPa 345 MPa 448 MPa

A992 345 MPa 448 MPa

18%

0.85 18%

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2.3 STANDARD CROSS-SECTIONAL SHAPES CATEGORY DESCRIPTION

HOT ROLLED: Wide Flange (W dxw) S-shape (S dxw) Channel (C dxw) Tee (WT dxw) Angle (L HxBxt)

BUILT UP

COLD FORMED: PLATE: Angle (BA HxBxt) Channel (BC HxBxt) LIGHT GAGE: Stiffened C (LC HxBxCxt) Stiffened Z (LZ HxBxCxt) Rec. Tube (LR HxBxt) Square Tube (LR HxBxt)

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DESIGN PRINCIPLES The design of a structural member entails the selection of a cross section that will safely and economically resist the applied loads. Economy means minimum weight—that is, the minimum amount of steel. 3.1 Design Basis (as per NSCP 2015) Designs shall be made according to the provisions for Load and Resistance Factor Design (LRFD) or to the provisions for Allowable Strength Design (ASD). 3.2 Limit States No applicable strength or serviceability limit state shall be exceeded when the structure is subjected to all appropriate load combinations such that: 𝑹𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒔𝒕𝒓𝒆𝒏𝒈𝒕𝒉 ≤ 𝒂𝒗𝒂𝒊𝒍𝒂𝒃𝒍𝒆 𝒔𝒕𝒓𝒆𝒏𝒈𝒕𝒉 Limit state can be fracture, yielding, buckling or serviceability such as maximum deflection depending on the type of element and support conditions. Strength can be tensile strength in tension members, compressive strength in columns, flexural strength or bending strength and shear strength in beams, etc. 3.3 ALLOWABLE STRENGTH DESIGN (ASD)  Member selection such that properties prevent the maximum applied loads or service loads to exceed an allowable or permissible value to maintain an elastic behavior  The allowable stress is the elastic range of the material  Member Selection by: o

Cross-sectional Area, A

o Moment of Inertia, I o Elastic Section Modulus, S NSC NSCP P Eq. 502 502.3.3.3-2 2 𝑹𝒂 ≤

𝑹𝒏 𝛀

𝒘𝒉𝒆𝒓𝒆: 𝑹𝒂 = 𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒔𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒃𝒂𝒔𝒆𝒅 𝒐𝒏 𝑨𝑺𝑫 𝒍𝒐𝒂𝒅 𝒄𝒐𝒎𝒃𝒊𝒏𝒂𝒕𝒊𝒐𝒏 𝑹𝒏 = 𝒏𝒐𝒎𝒊𝒏𝒂𝒍 𝒔𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒃𝒂𝒔𝒆𝒅 𝒐𝒏 𝒍𝒊𝒎𝒊𝒕 𝒔𝒕𝒂𝒕𝒆 𝛀 = 𝒇𝒂𝒄𝒕𝒐𝒓 𝒐𝒇 𝒔𝒂𝒇𝒆𝒕𝒚 𝒃𝒂𝒔𝒆𝒅 𝒐𝒏 𝒍𝒊𝒎𝒊𝒕 𝒔𝒕𝒂𝒕𝒆 𝑹𝒏 = 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑜𝑟 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝛀

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3.4 LOAD AND RESISTANCE FACTOR DESIGN (LRFD)  Design based on failure mode or limiting state  Loads are factored to bring the members to its limit state or failure but safe under service loads  Design strength is nominal strength multiplied by a reduction factor or resistance factor  Resistance factor defines the usable or permissible strength and is less that 1.0

NSC NSCP P Eq. 502 502.3.3.3-2 2 𝑹𝒖 ≤ 𝝓𝑹𝒏 𝒘𝒉𝒆𝒓𝒆: 𝑹𝒖 = 𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒔𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒃𝒂𝒔𝒆𝒅 𝒐𝒏 𝒇𝒂𝒄𝒕𝒐𝒓𝒆𝒅 𝒍𝒐𝒂𝒅 𝒄𝒐𝒎𝒃𝒊𝒏𝒂𝒕𝒊𝒐𝒏 𝑹𝒏 = 𝒏𝒐𝒎𝒊𝒏𝒂𝒍 𝒔𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒃𝒂𝒔𝒆𝒅 𝒐𝒏 𝒍𝒊𝒎𝒊𝒕 𝒔𝒕𝒂𝒕𝒆 𝝓 = 𝒓𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒇𝒂𝒄𝒕𝒐𝒓 𝒃𝒂𝒔𝒆𝒅 𝒐𝒏 𝒍𝒊𝒎𝒊𝒕 𝒔𝒕𝒂𝒕𝒆 𝝓𝑹𝒏 = 𝑑𝑒𝑠𝑖𝑔𝑛 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 3.5 LOAD COMBINATION 3.5.1 LRFD COMBINATION NSCP 203.3.1 𝑈1 = 1.4𝐷 𝑤ℎ𝑒𝑟𝑒 𝑓1 = 1.0 𝑓𝑜𝑟 𝑝𝑙𝑎𝑐𝑒 𝑜𝑓 𝑝𝑢𝑏𝑙𝑖𝑐 𝑎𝑠𝑠𝑒𝑚𝑏𝑙𝑦, 𝑈2 = 1.2𝐷 + 1.6𝐿 𝑙𝑖𝑣𝑒 𝑙𝑜𝑎𝑑𝑠 > 4.8𝑘𝑃𝑎, 𝑎𝑛𝑑 𝑔𝑎𝑟𝑎𝑔𝑒 𝑈3 = 1.2𝐷 + 1.0𝑊 + 𝑓1 𝐿1 𝑓1 = 0.5 𝑓𝑜𝑟 𝑜𝑡ℎ𝑒𝑟 𝑙𝑖𝑣𝑒 𝑙𝑜𝑎𝑑𝑠 𝑈4 = 1.2𝐷 + 1.0𝐸 + 𝑓1 𝐿1 𝑈5 = 0.9𝐷 + 1.0𝑊 𝑈6 = 0.9𝐷 + 1.0𝐸 3.5.2 ASD BASIC LOAD COMBINATION 𝑆1 = 𝐷 𝑆2 = 𝐷 + 𝐿 𝑆3 = 𝐷 + 0.6𝑊 𝐸 𝑆4 = 𝐷 + 1.4 3.5.3 ASD ALTERNATE LOAD COMBINATION 𝑆1 = 𝐷 + 𝐿 The 0.75 factor is used as a one𝑆1 = 0.75(𝐷 + 𝐿 + 0.6𝑊) 𝐸 third increase in allowable 𝑆2 = 0.75 (𝐷 + 𝐿 + ) stresses shall be permitted for 1.4 all combinations with W or E. 𝑆3 = 0.6𝐷 + 0.6𝑊 𝐸 𝑆4 = 0.6𝐷 + 1.4

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TENSION MEMBERS Tension members are structural elements designed to resist axial tensile forces. Common tension members are truss members (bottom chords and webs), bracing of braced frames in buildings and bridges, suspension cables in roofs and bridges. The stress in any tension member is 𝒇=

𝑷

𝑨

so the only determinant of the strength is the cross-sectional area. Circular rods and rolled angle shapes are commonly used. Connecting these members to other members may be by bolts, rivets or welds. The presence of holes (to accommodate bolts or rivets) reduces the area resisting the stress and affects the performance of the tension member. 4.1 LIMIT STATES A tension member can fail by two limiting states or mode of failure:



Net Area – reduced gross area due to existing holes



Effective Net Area – reduced net area to account for non-uniform stress distribution when not all parts of the member is connected

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GROSS AREA

𝐵 𝑤𝑔

𝑡⬚

𝐻 𝑡⬚

𝑡𝑝

𝐴𝑔 = 𝑤𝑔 × 𝑡𝑝

𝑤𝑔 = 𝐵 + 𝐻 − 𝑡⬚ 𝑡𝑝

𝐴𝑔 = 𝑤𝑔 × 𝑡⬚

Local standard shapes that are commercially available have their properties calculated and tabulated in the ASEP Steel Handbook. NET AREA When tension members are connected to other members or spliced by bolts or rivets, holes are punched creating a reduction in the cross-sectional area. Across holes, normal to the direction of the load fracture or rupture is expected to occur. The net area, 𝐴𝑛 , is then calculated as the gross area less the projected area of the holes with each hole area equal to efffective hole diameter multiplied by thickness of the member. 𝑡𝑝 𝑑𝑒 𝑑𝑒

rupture line 𝑑𝑏

𝑡𝑝

𝑑𝑛 𝑑𝑒

𝑑𝑏 = 𝑏𝑜𝑙𝑡 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑑𝑛 = 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 ℎ𝑜𝑙𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑑𝑒 = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 ℎ𝑜𝑙𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑤𝑔

𝑑𝑒

Projected area of hole = 𝑑𝑒 × 𝑡𝑝

𝑑𝑒

𝐴𝑛 = 𝑤𝑛 × 𝑡𝑝 𝑤𝑛 = 𝑤𝑔 − 𝑛 × 𝑑𝑒 Alternately, 𝐴𝑛 = 𝐴𝑔 − 𝑛 × 𝑑𝑒 × 𝑡𝑝 Where: 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ℎ𝑜𝑙𝑒𝑠 𝑎𝑐𝑟𝑜𝑠𝑠 𝑎 𝑟𝑢𝑝𝑡𝑢𝑟𝑒 𝑙𝑖𝑛𝑒

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NSCP 2015

It can be observed from Table 510.3.3 of NSCP that bolts under 24 mm will require a nominal hole diameter of 𝑑𝑛 = 𝑑𝑏 + 2 𝑚𝑚 and bolts 24 mm and larger will have 𝑑𝑛 = 𝑑𝑏 + 3 𝑚𝑚. Furthermore, for

the calculation of net area (in tension and shear) the bolt hole (damaged hole) diameter is: 𝑑𝑒 = 𝑑𝑏 + 4 𝑚𝑚 for 𝑑𝑏 < 24 𝑚𝑚 𝑑𝑒 = 𝑑𝑏 + 5 𝑚𝑚 for 𝑑𝑏 ≥ 24 𝑚𝑚

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