## Info

A See Table 4.8 for definitions of the terms used, and replace Fy by iy for hybrid sections. a See Table 4.8 for definitions of the terms used, and replace Fy by iy for hybrid sections. Moreover, the structure needs to be designed for loads and load combinations that include the effect of earthquakes, and if the applicable building code (e.g., UBC 1997 IBC 2000) requires that amplified seismic loads be used, the horizontal component of the earthquake load shall be multiplied by an overstrength...

## 106 Diaphragms

To be designed for equal magnitude torsion and compression forces. When the seismic forces are acting at 90 to the original direction analyzed, the chords act as the struts for the diaphragm to transfer the reaction loads to the shear walls below. If the shear walls are not continuous along the length of the diaphragm, then the strut may act as the drag strut between the segments of the shear wall as well. Diaphragms often have openings to facilitate stairwells, great rooms that are more than...

## 183 Damage as a Result of Structural Problems 1831 Foundation Failure

Usually, it is the connection to the foundation or an adjacent member rather than the foundation itself that is damaged during a large earthquake. However, materials that cannot resist lateral forces, such as hollow masonry blocks, make a poor foundation and their use should be avoided (Figure 18.32). Engineers will occasionally design foundations to rock during earthquakes as a way of dissipating energy and of reducing the demand on the structure. However, when the foundation is too small, it...

## 22

Calculate G-factor for the member BC using Equation 31.81. E (1 L)nr mn (1.21 L)(-0.312)(1.5) Comparing with the assumed KAB 1.20 it is alright. 8. It is seen that the largest set of K-factors is 31.5.6 Consideration of Partial Column Base Fixity In computing the effective length factor for monolithic connections, it is important to properly evaluate the degree of fixity in foundation. The following two approaches can be used to account for foundation fixity. 31.5.6.1 Fictitious Restraining...

## 323 Background

Structural bracing used to increase the strength of members must possess both sufficient strength and stiffness 2 . Simple bracing design rules such as designing a brace to resist 2 of the member compressive force address only the strength criterion. The stiffness of the brace along with the out-of-straightness of the member has a direct effect on the magnitude of the brace force 1 . Design recommendations based on perfectly straight members should not be used directly in design since extremely...

## 1941 Wood Frame

Wood-frame structures tend to be mostly low rise (one to three stories, occasionally four stories). Vertical framing may be of several types, for example, stud wall, braced post and beam, or timber pole Stud walls are typically constructed of 2 in. by 4 in. wood members vertically set about 16 in. apart multiple story buildings may have 2 x 6 or larger studs. These walls are braced by plywood sheathing or by diagonals made of wood or steel. Most detached single and low-rise multiple family...

## 123 Introduction of the Reliability Based Structural Design Concept

The design aids in AISC's LRFD and ASD guidelines are very similar. In both approaches, the isolated member approach was used to develop the design guidelines 11 . There are several advantages to the isolated-member approach (1) in deterministic design methods that use safety factors, it is not practical to prepare detailed requirements for each structural configuration (2) the characteristics of the individual members and connections are independent of the framework and (3) most research has...

## Bfd

FIGURE 20.11 Methods of minimizing damage to abutment foundation 37 . The SDC shown in Table 20.2 shall be achieved by the following design objectives All bridges shall be designed to withstand deformation imposed by the design earthquake. All structure components have sufficient strength and ductility to ensure collapse will not take place during the maximum credible earthquake (MCE). Ductile behavior can be provided by inelastic actions either through selected structural members and through...

## 23 Trusses

A structure that is composed of a number of members pin-connected at their ends to form a stable framework is called a truss. If all the members lie in a plane, it is a planar truss. It is generally assumed that loads and reactions are applied to the truss only at the joints. The centroidal axis of each member is straight, coincides with the line connecting the joint centers at each end of the member, and lies in a plane that also contains the lines of action of all the loads and reactions....

## Example

Suppose a plane stress condition exists, derive the equations for (1) stress transformation, (2) principal stresses, and (3) principal planes for this condition. 1. Stress transformation. With reference to Figure 1.4, a direct application of Equation 1.9, with the condition s33 s23 s13 0 applying to a plane stress condition, gives the following stress transformation equations s'n o-n cos20 + s22 cos2 (90 0) + s12 cos 0 cos(90 0) + s21 cos(90 0) cos 0 s22 s11 cos2 (90 + 0) + s22 cos20 + s12...

## 20624Force Demands on Capacity Protected Components

Seismic demands on capacity-protected components, such as superstructures, bent caps, and foundations, are measured in terms of forces rather than displacements. Force demands for capacity-protected components shall be determined by the joint-force equilibrium considering plastic hinging capacity of the ductile component multiplied by an overstrength factor of 1.2. The overstrength factor accounts for the possibility that the actual ultimate plastic moment strength of the ductile component...

## JpDDDDDDD

FIGURE 25.47 Type of Rahmen bridges (a) portal frame (b) p-Rahmen (c) V-leg Rahmen and (d) Vierendeel Rahmen. finite element analyses or experimental verification. The supports of Rahmen bridges are either hinged or fixed, making it an externally indeterminate structure, and it is therefore not suitable when the foundation is likely to sink. The reactions at supports are horizontal and vertical forces at hinges, and with the addition of a bending moment at a fixed base. A portal frame is the...

## 4

The subdivision of the surface of the braced dome can also be carried out using the following three methods. The first method is based on the surface of revolution, and the first set of lines of division are drawn as the meridional lines from the apex. Next, circumferential rings are added. This results in a ribbed dome and further a Schwedler dome. Alternately, the initial set maybe taken as a series of spiral arcs, resulting in dividing the surface into triangular units as uniform as...

## 69 87 55 72 92

Based on the recommended acceptance criteria, it is deduced that the confidence level associated with preventing building collapse at the computed drift values is extremely high (actually, this value is at its upper limit). However, the confidence level on IO performance is unacceptable. The minimum recommended value in FEMA-350 is 50 , while the confidence levels based on computed interstory drift are well below these limits for the first five story levels. Unfortunately, FEMA-350 does not...

## 242 Double Layer Grids 2421 Types and Geometry

Double-layer grids, or flat surface space frames, consist of two planar networks of members forming the top and bottom-layers parallel to each other and interconnected by vertical and inclined web members. Double-layer grids are characterized by hinged joints with no moment or torsional resistance therefore, FIGURE 24.3 Basic elements of double-layer grids. FIGURE 24.3 Basic elements of double-layer grids. all members can only resist tension or compression. Even in the case of connection by...

## R

This theorem applies only to structures stressed within the elastic limit and all deformations must be linear homogeneous functions of the loads. For a beam in equilibrium as in Figure 2.63, the total potential energy is U - Piyi + P2y2 + + PjYj + + Pnyn + V (2.117) For an elastic system, the strain energy, V, turns out to be one half the change in the potential energy of the loads Castigliano's Theorem results from studying the variation in the strain energy, V, produced by a differential...

## 2432 Braced Barrel Vaults

The braced barrel vault is composed of member elements arranged on a cylindrical surface. The basic curve is a circular segment occasionally, a parabola, ellipse or funicular line may also be used. Figure 24.12 shows the typical arrangement of a braced barrel vault. Its structural behavior depends mainly on the type and location of supports, which can be expressed as L R, where L is the distance between the supports in longitudinal direction and R is the radius of curvature of the transverse...

## 2764 Nonlinear Analysis

Advances in the analyses of reinforced concrete have produced the capability to analyze shells taking into account the layered composition of the cross-section as shown in Figure 27.28. Using realistic material properties for steel and for concrete, including tension stiffening in the form shown in Figures 27.29 to 27.32, fto yield stress in tension fco yield stress in compression 0 modulus of elasticity Et tangent modulus of elasticity fto yield stress in tension fco yield stress in...

## 852

continuous beam by moment distribution. FIGURE 2.23 Example Copyright 2005 by CRC Press continuous beam by moment distribution. B-ends of spans BA and BC in proportion to their distribution factors. The values of these distributed moments are carried over at one-half rate to the other ends of the members. When equilibrium is reached, joint B is clamped in its new rotated position and joint C is released afterward. Joint C rotates under its unbalanced moment until it reaches equilibrium, the...

## Csu

FIGURE 22.22 (a) Rectangular grid layout. (b) Preferred and nonpreferred grid layouts. The analysis and design of a simple braced frame must recognize the following points 1. The members intersecting at a joint are pin connected. 2. The columns are not subjected to any direct moment transferred through the connection, but nominal moments due to eccentricity of the beam reaction forces should be considered. The design axial force in the column is predominately governed by floor loading and the...

## 319 Latticed and BuiltUp Members

The main difference of behavior between solid-webbed members and latticed members and built-up members is the effect of shear deformation on their buckling strength. For solid-webbed members, shear deformation has a negligible effect on their buckling strength, while for latticed structural members using lacing bars and batten plates, shear deformation has a significant effect on their buckling strength. It is common practice that when the buckling model involves relative deformation produced...

## 1945Configuration Irregularities and Pounding

Certain problems in earthquake performance are common to many building types and include issues of configuration, irregularities, and pounding. 19.4.5.1 Configuration and Irregularities Configuration, or the general vertical and or horizontal shape of buildings, is an important factor in earthquake performance and damage. Buildings that have simple, regular, symmetric configurations generally display the best performance in earthquakes. The reasons for this are (a) nonsymmetric buildings tend...

## 296Numerical Examples for Breakage Analysis of Glass Structure

Any numerical or analytical method must first be tested and validated before it can be actually used. The limitations and scopes of the method must be clearly investigated and defined. This chapter presents a verification study on the application of the developed finite element method for several nonlinear problems for glass structures. The accuracy of the developed method is then compared with the available solution. The first example is to compare the results of in-service glass obtained by...

## 10

FIGURE 22.53 Power spectrum of longitudinal turbulence. for the fundamental frequency of a tall building is 0.1 to 1 Hz, the buildings are affected by high-frequency small eddies characterizing the descending part of the power spectrum. 22.5.2.5 Cross-Spectrum of Turbulence The cross-spectrum of two continuous records is a measure of the degree to which the two records are correlated. If the records are taken at two points M1 and M2 separated by a distance r, then the cross-spectrum of...

## P A

In this equation, Px is the dead weight of the structure above story x, A is the design story drift, computed from Equation 19.22, Vx is the design story shear obtained from the lateral force analysis, hx is the story height, and Cd is the coefficient previously discussed. If the quantity 6 computed by this equation is found to be less than 0.1, P-A effects may be neglected. If the quantity 6 is greater than 0.1, P-A effects must be directly considered in performing the LFA. If the quantity 6...

## 085

Where Pu is the required column strength and Py is the column squash load. The connections details used to attach structural bracing members can be of great importance when designing or evaluating the overall performance of a bracing system. If the connections are flexible, the stiffness of the overall bracing system can be significantly less than the stiffness of the bracing member alone. The stiffness of a bracing system can be evaluated as springs in series using The system stiffness, bsys,...

## 1615 Design of Pultruded Structural Connections

Pultruded FRP sections can be used in trusses and braced frame structures. As with the design of FRP structural sections there is no design guide or code for connections for pultruded structures. Connections are currently designed based on the first principles of mechanics and tests of full-sized connections. For common FRP pultruded sections mechanical fasteners (bolts, rivets, screws) and adhesive bonding (epoxy, polyester) are most commonly used. Both steel and FRP bolts are available...

## 2g14 Table 2g1

Handbook of Structural Engineering Recommended LRFD Guidelines. Design Earthquakes and Seismic Performance Objectives 37 Probability of exceedance for design earthquake ground motions Rare earthquake (MCE) 3 PE in 75 years 1.5 mean deterministic Expected earthquake 50 PE in 75 years a The upper-level earthquake considered in the Guidelines is designated the Maximum Considered Earthquake or MCE. In general the ground motions or national MCE ground motion maps have a probability of exceedance...

## 1835 Shear

Most building structures use shear walls or moment-resisting frames to resist lateral forces during earthquakes. Damage to these systems varies from minor cracks to complete collapse. Figure 18.48 is a photo of the Mt. McKinley Apartments after the 1964 Great Alaska Earthquake. It was a 14-story RC building composed of narrow exterior shear walls and spandrel beams (Figure 18.48), as well as interior and exterior columns and a central tower. During the 1964 earthquake, this structure suffered...

## 153634Processing Methods

The commonly used processing methods in industries include hatschek process, reticem process, continuous surface reinforced process, wellcrete process, normal casting, pultrution process, and extrusion process. The extrusion technology is an economical mass-production method. The advantage of introducing extrusion into processing of cement products is that the materials are formed under high shear and high compressive forces. With properly designed dyes and properly controlled material mixes...

## 34211 Standard SN Curves

The nominal stress approach is the established approach for fatigue design and assessment of steel and aluminum structures. The nominal stress approach is based on S-N curves, where S is the nominal stress range and N is the number of cycles until the appearance of a visible crack. Details are designed based on the nominal stress range in the connecting members rather than the local ''concentrated'' stress at the detail. The nominal stress is usually obtained from standard design equations for...

## 2

4.12.1.2 Base Plates for Tubular and Pipe Columns The design concept for base plates discussed above for I-shaped sections can be applied to the design of base plates for rectangular tubes and circular pipes. The critical section used to determine the plate thickness should be based on 0.95 times the outside column dimension for rectangular tubes and 0.80 times the outside dimension for circular pipes (Dewolf and Ricker 1990). 4.12.1.3 Base Plates with Moments For columns in frames designed to...

## 40 H

FIGURE 3.39 Effect of ps on xs versus time. (Reprinted from Ref. 1, p. 547 by courtesy of Marcel Dekker, Inc.) FIGURE 3.39 Effect of ps on xs versus time. (Reprinted from Ref. 1, p. 547 by courtesy of Marcel Dekker, Inc.) versus time are shown in Figure 3.39. Note that p 1 is corresponding to elastic response and p 0.001 is close to elasto-plastic case, more decreases in ps and more increases in deflections. 3.7.5 Effects of P-A, Material Nonlinearity, and Large Deformation on Response The...

## 7

Further details can be obtained from Yang and Kuo (1994). 2.12.11 Buckling of Thin Plates 2.12.11.1 Rectangular Plates The main difference between columns and plates is that quantities such as deflections and bending moments that are functions of a single independent variable in columns become functions of two independent variables in plates. Consequently, the behavior of plates is described by partial differential equations, whereas ordinary differential equations suffice for describing the...

## W3 Theorem Civil Engineering

The matrix F is called the flexibility matrix. It can be shown, by applying Maxwell's reciprocal theorem (Borg and Gennaro 1959), that the matrix F is a symmetric matrix. Let us consider a cantilever beam loaded as shown in Figure 2.70a. The first column in the flexibility matrix can be generated by applying a unit vertical load at the free end of the cantilever as shown in Figure 2.70b and making use of the moment-area method. We get

## 134

4.11.2.7 Welded Connections With Welds Subjected to Combined Shear and Flexure Figure 4.24 shows a welded framed connection and a welded seated connection. The welds for these connections are subjected to combined shear and flexure. For purpose of design, it is common practice to assume that the shear force per unit length, RS, acting on the welds is a constant and is given by where P is the allowable load (in ASD), or factored load, Pu (in LRFD), and l is the length of the vertical weld. In...

## Wrr

FIGURE 31.6 Diagonal cross bracing system. FIGURE 31.6 Diagonal cross bracing system. 31.4.2.3 Threshold Lateral Stiffness of Braces For a multistory braced frame, Tong and Shi (2001) defined the threshold lateral stiffness as the bracing stiffness at which the critical buckling load in sway buckling mode is equal to the nonsway buckling mode. They found out that most threshold stiffness values are from p2 to 4p2 and proposed the following approximate formula (Tong and Shi 2001) where Kb and...

## 046

FIGURE 27.13 Harmonic components of the radial displacement. The dynamic amplification of the effective velocity pressure is represented by the parameter g in Equation 27.5. This parameter reflects the resonant part of the response of the structure and may be as much as 0.2, depending on the dynamic characteristics of the structure. However, when the basis of q(z) includes some dynamic portion such as the fastest-mile-of-wind, (1 + g) is commonly taken as 1.0. Cooling towers are often...

## L

W Nonintegral rigid wall u Integral rigid wall FIGURE 28.2 Typical sections for cut-and-cover tunnels. Cut-and-cover tunnel sections are most often modeled as structural frames. In general, however, there are three ways to analyze cut-and-cover tunnel sections Traditional frame analysis. A stick figure is drawn to represent the tunnel section. Soil-structure interaction is treated as an applied load to the frame. Frame analysis with a more rigorous soil-structure interaction. The soil is not...

## 30 20 10 00 10 20

FIGURE 13.19 Drag force coefficient distribution of the model for measurement in the staggered arrangement of viaducts without noise barrier (a) mean value and (b) mean value plus fluctuation (root mean square). FIGURE 13.20 Drag force coefficient distribution of the model for measurement in the staggered arrangement of viaducts without noise barrier (a) mean value and (b) mean value plus fluctuation (root mean square). and without noise barrier, the mean value for both cases is almost equal....

## Vpp

1 2 Dia. anchor bolt at 42 o.c. for shear and uplift (378 klf) (Check axial strength and size plate washer) 1 2 Dia. anchor bolt at 42 o.c. for shear and uplift (378 klf) (Check axial strength and size plate washer) Metal plate connector (e.g., 35 F at 42 o.c.)' Metal plate connector (e.g., 35 F at 42 o.c.)' 1 2 Dia. anchor bolt at 42 o.c. for shear 1 2 Dia. anchor bolt at 42 o.c. for shear FIGURE 10.14 Details for perforated shear wall (Example 10.2). Strap at 2'-0 o.c. for uplift (730 klf) or...

## 101 Introduction

Stone and wood were the first materials used by man to build shelter, and in the United States wood continues to be the primary construction material for residential and commercial buildings today. In California, for example, wood accounts for 99 of residential buildings (Schierle 2000). Design and construction methods for wood currently used by the residential construction industry in North America have developed through a process of evolution and tradition. Historically, these construction...

## Dst

As & e R Ay Ad Cd As FIGURE 21.1 Conceptual basis behind use of R-factors. may delay initial yielding beyond this value. Hence, the actual force-reduction factor or response modification factor as defined in IBC (2000) can be defined as follows The ratio Ce Cy can be viewed as the response modification factor related to ductility (Rm), while the ratio Cy Cs contains two components overstrength (RQ and redundancy (Rr). Hence, the R-factor can be broken down into three main components as...

## 022

An important property of glass is that its strength depends on the duration of load 6 application and on the environmental conditions. This concept is not familiar to engineers and architects. Basically, the relationship between stress and time can be expressed as where a is the applied stress, while T is the duration of the stress, and n is a constant with a value between 12 and 20. Figure 29.6 illustrates the strength of glass against time. Since the duration of loading is Preferential attack...

## 1624 Design of Flexural Members with FRP Reinforcing Bars 16241 Moment Capacity

Design of flexural members follows the strength design method of the ACI limit states version of an LRFD design basis. In this approach the nominal factored moment resistance (f Mn) of the member must be greater than the factored ultimate moment required (Mu). The nominal moment capacity of FRP reinforced concrete members is determined in a similar fashion to that of a steel reinforced section however, since FRP rebars do not yield (i.e., are linear elastic to failure), the ultimate strength of...

## O

FIGURE 22.10 Tapered composite beam. Haunched beams are designed by forming a rigid moment connection between the beams and columns. The haunch connections offer restraints to beam and it helps to reduce mid-span moment and deflection. The beams are designed in a manner similar to continuous beams. Considerable economy can be gained in sizing the beams using continuous design that may lead to a reduction in beam depth up to 30 and deflection up to 50 . The...

## 202 Earthquake Damages to Bridges

Past earthquakes have shown that the damage induced in bridges can take many forms depending on the ground motion, site conditions, structural configuration, and specific details of the bridge 1 . Damage within the superstructure has rarely been the primary cause of collapse. Most of the severe damage to bridges has taken one of the following forms 1 Unseating of the superstructure at in-span hinges or simple supports due to inadequate seat lengths or restraint. A skewed, curved, or complex...

## 2624 End Fittings of Cable

Bridge cables are connected and anchored to the anchoring substructures or other structural members such as the girder and towers through the end fittings. For parallel-wire cables erected by the air-spinning method, the anchoring is generally made by looping the wires around a strand shoe disc that is semicircular or circular and is fixed to the anchor frame through anchoring rods. 26.2.4.2 Metallic Alloy Sockets For prefabricated strands, either parallel-wire cables or wire ropes, both ends...

## 305 Failure Modes

A number of unique failure modes are possible in tubular connections. In addition to the usual checks on weld size, provided for in most design codes, the designer must check for the following failure modes, listed together with the relevant AWS and AISC Code sections. Local failure (punching shear) General collapse Unzipping (progressive weld failure) Materials problems Fracture Delamination Fatigue 2.24.1.3 Ref. to AWS 2.26 C4.12.4.4 C2.6.3 2.36.6 AWS design criteria for this failure mode...

## 2341 End Fixity Factor of Semirigid Member

Shown in Figure 23.6 is a semirigid member comprising a finite-length beam-column member with a zero-length rotational spring at each end (the symbol represents the spring). The connection flexibilities are modeled through rotational springs of stiffness R1 and R2 at the two ends of the beam. The relative stiffness of the beam-column member and the rotational end-spring connection is measured by an end-fixity factor defined as follows 21 where Rj is the end-connection spring stiffness and EI L...

## 326 Beam Bracing

Structural bracing for beams can be generally classified as either a lateral or a torsional system. Lateral beam bracing, like column bracing, can be relative, nodal, continuous, or lean-on while torsional systems can be nodal or continuous. Cross-frames or diaphragms connecting adjacent girders control twist of the cross-section and represent purely torsional systems. Similarly, joists attached to the compression flange of a simply supported beam control twist by preventing the lateral...

## V

Compression normal to effective area Tension or compression parallel to axis of weld Shear on effective area Compression normal to effective area Tension or compression parallel to axis of weldd Tension or compression parallel to axis of weldd Shear parallel to faying surfaces (on effective area) Full penetration groove weld Base Same as base metal 0.90Fy Base Same as base metal 0.90Fy Weld strength of weld metal electrode Weld strength of weld metal electrode Base 0.30 x nominal tensile Weld...

## 1954 Seismic Design Categories

The seismicity of the United States, and indeed the world, varies widely. It encompasses zones of very high seismicity in which highly destructive levels of ground shaking are anticipated to occur every 50 to 100 years and zones of much lower seismicity in which only moderate levels of ground shaking are ever anticipated. The NEHRP Provisions recognize that it is neither technically necessary nor economically appropriate to require the same levels of seismic protection for all buildings across...

## N

m + c _ + k - Rn g (21.A4) Comparing Equation 21.A4 to Equation 21.A2 and following through with the modal transformation that results in Equation 21.A3, it can be shown that Each term in the above expansion contains the modal contribution of the respective mode. Another way of visualizing Equation 21.A5 is to consider the load vector on the right-hand side of Equation 21.A2 as follows where R is a load distribution vector. For a general loading function p(t) r (f), the vector r represents a...

## 13

Factored forces in tendon rows and bearing capacity of the concrete. From Equation 8.32c for low-relaxation strands, fpi 0.80 pu. The factored jacking force at the short jacking time interval is Psu 1.2Aps (0.80fpu) 0.96fpu Aps 0.96 x 270,000 259,200 psi. If stress-relieved strands are used, it would have been advisable to use fpi 0.70 pu first row force Pu1 5 x 0 .153 x 259,200 198,286 lb (882 kN) second row force Pu2 5 x 0 .153 x 259,200 198,286 lb (882 kN) third row force Pu3 3 x 0 .153 x...

## Gx

(D Reel (tension control) (2) Spinning wheel Live wire guide roller FIGURE 26.14 Operating principle of tension control method. (Source Honshu-Shikoku Bridge Authority, Technology of the Seto-Ohashi Bridge, Japan, 1989, with permission.) (D Reel (tension control) (2) Spinning wheel Live wire guide roller FIGURE 26.14 Operating principle of tension control method. (Source Honshu-Shikoku Bridge Authority, Technology of the Seto-Ohashi Bridge, Japan, 1989, with permission.) The erection of the...

## 1834 Torsional Moments

Curved, skewed, and eccentrically supported structures often experience a torsional moment during earthquakes. FIGURE 18.37 Soft story collapse in San Francisco during the 1989 Loma Prieta Earthquake. (Photo courtesy of the USGS The Loma Prieta, USGS, 1998.) FIGURE 18.37 Soft story collapse in San Francisco during the 1989 Loma Prieta Earthquake. (Photo courtesy of the USGS The Loma Prieta, USGS, 1998.) A nine-story building in Kobe, Japan, consisted of shear walls along three sides and a...

## T

FIGURE 8.2 Double tee pretensioned beam in Example 1 (a) elevation and (b) pretensioned section 5 . WL 40 psf (1,915 Pa) transient fpy 0 . 85fpu 230,000 psi (1,589 MPa) fpi 0 . 70fpu 0 . 82 py 0 .82 x 0 . 85 Pu ffi 0 .70 Pu 189,000 psi (1,303 MPa) Eps 28 x 106 psi (193 .1 x 106 MPa) 18-day modular ratio 9 . 72 Aa 4 in . 0 . 25 in., L 70 ft The anchorage slip stress loss is A pa Eps -x 28 x 106 ffi 8333 psi (40 . 2 MPa) 2. Elastic shortening. Since all jacks are simultaneously posttensioned, the...

## 0024489

Direct Monte Carlo simulation method cannot accurately predict the probability of failure. However, as the number of simulation cycles increases, the probability of failure approaches the value obtained using FORM. The important conclusion is that MVFOSM should not be used for structural reliability evaluation. Columns 4 and 5 give the probabilities of failure using the conditional expectation VRT and conditional expectation plus antithetic variates VRT. The results indicate the power of the...

## 263 Suspension Bridges 2631 Structural System

26.3.1.1 Components of a Suspension Bridge A suspension bridge typically consists of the following components (Figure 26.6) 1. Main cables that suspend the bridge deck. 2. Main towers that support the main cables. Sometimes lower subtowers are positioned between the main tower and the cable anchorage to lead the cable to the anchorage. 3. Stiffening girder, either solid-web girder or truss, being incorporated with the bridge deck. 4. Hangers or suspenders that connect the bridge deck with the...

## 1854 Structural Elements that Prevent Damage and Improve Dynamic Response

Improved structural performance during large earthquakes depends on a balanced structural system. Elements that share the same displacement during large earthquakes must be designed to have about the same stiffness. Otherwise, the stiffer elements will be forced to resist most of the earthquake force. Elements that share the same force are often provided with a fuse to limit the force and protect adjacent members. Providing great strength to resist earthquakes is usually self-defeating. As the...

## 41

4.1.1 Stress-Strain Behavior of Structural Steel Structural steel is a construction material that possesses attributes such as strength, stiffness, toughness, and ductility that are desirable in modern constructions. Strength is the ability of a material to resist stress. It is measured in terms of the material's yield strength Fy and ultimate or tensile strength Fu. Steel used in ordinary constructions normally have values of Fy and Fu that range from 36 to 50 ksi (248 to 345 MPa) and from 58...

## References

Chapter 34 Earthquake Damage to Bridges, Bridge Engineering Handbook, ed., Chen, W.F. and Duan, L., CRC Press, Boca Raton, FL, 2000. 2 Yashinsky, M. Chapter 29a Earthquake Damage to Structures, Structural Engineering Handbook CRCnetBase 2000, ed., Chen, W.F. and Duan, L., CRC Press, Boca Raton, FL, 2000. 3 Housner, G.W. Competing Against Time, Report to Governor George Deuknejian from The Governor's Broad of Inquiry on the 1989 Loma Prieta Earthquake,...

## Fti

Where De is the total strain range, su is the tensile strength, and ef is the elongation at fracture. FIGURE 34.8 Low-cycle fatigue crack developing at the end of the beam web to column flange weld in a momentframe connection. FIGURE 34.8 Low-cycle fatigue crack developing at the end of the beam web to column flange weld in a momentframe connection. FIGURE 34.9 Low-cycle fatigue crack developing at the weld access hole in a moment-frame connection. FIGURE 34.9 Low-cycle fatigue crack developing...

## Qaw

FIGURE 24.23 Wind pressure coefficients for arched roof. Notes (a) For 0 < h d < 0.5, cpe> 10 is obtained by linear interpolation (b) for 0.2 < f d < 0.3 and h d > 0.5, two values of Cpe> 10 have to be considered and (c) the diagram is not applicable for slat roofs. FIGURE 24.23 Wind pressure coefficients for arched roof. Notes (a) For 0 < h d < 0.5, cpe> 10 is obtained by linear interpolation (b) for 0.2 < f d < 0.3 and h d > 0.5, two values of Cpe> 10 have to be...

## 3010 Summary and Conclusions

This chapter has served as a brief introduction to the subject of designing welded tubular connections for circular hollow sections. More details on the background and use of AWS, AISC, and international codes in this area can be found inRef. 12 , on the Internet 13,14 , and bye-mail to the source 4 of these criteria 15 . 1 AWS D1.1-2002. 2002. Structural Welding Code-Steel, American Welding Society, Miami, FL. 2 AISC. 1997. Hollow Structural Sections Connections Manual, joint publication of...

## 1

(npApsdp + nsAsd2 - 1. 6 Jnppp + np aw 8 .48 X 10-5 for pretensioned 9 .44 X 10-5 for posttensioned 4 .0 X 10-5 for concretes with fc' > 70 MPa MPa N mm2 (psi) 0 .006895 MPa (lb ft) 14.593 N m (in. lb) 0 .113 N m The author wishes to acknowledge the permission granted by Prentice Hall, Upper Saddle River, New Jersey, and Ms Marcia Horton, its vice president and publications director, to use several chapters of his book, Prestressed Concrete A Fundamental Approach, 4th Edition, 2003, 944 pp....

## Example 3612

The support beams in the retaining wall in Example 36.11 are European wide-flange beams HE 180 M having a yield strength of 355 MPa. The initial dimensions of the beam as shown in Figure 36.7 are b 186mm, h 200 mm, tw 14.5 mm, and tf 24mm. Apply the thickness loss from Example 36.11 to reflect the loss in moment capacity in the I-beam after 10 years. After 20 years. The plastic moment capacity of the beam is the product of the yield strength and the plastic section modulus. Because the beam and...

## Example 326

Design the diagonals of the top flange horizontal truss to stabilize the five simply-supported 90 ft girders. The factored moment at midspan Mu 1200 k ft and Fy 36 ksi for bracing. COS20 ( Abr(29> 000)_) (ffi) 2 18.1 (1200 x 12)(1.0) . , . Pbr 0.008 - '- (2.5 girders) 5.88 k The primary factors influencing the effectiveness of lateral beam bracing have relatively little influence on the design of torsional beam bracing. Unlike lateral beam bracing, the number of braces, brace location on the...

## 2642 Configuration and Design of Structural Components

Since the types, corrosion protection, and vibration control of cables were already mentioned in Section 26.2, just the anchoring techniques of cables in cable-stayed steel bridges will be reviewed herein. The structural details to anchor stay cables at the main girder or the tower shall be designed so as to smoothly transmit cable tension to the main structural component, to be as simple and compact as possible, to be easy in fabrication and maintenance, and to have good appearance. Care shall...

## 714 Columns

Typical reinforcement concrete columns are shown in Figure 7.21. Longitudinal reinforcements in columns are generally distributed uniformly around the perimeter of the column section and run continuously through the height of the column. Transverse reinforcement may be in the form of rectangular hoops, ties, or spirals (Figure 7.21). Tall walls and core elements in buildings (Figure 7.22) are column-like in behavior and the design procedures presented in the following are applicable. FIGURE...

## Tunnel Jacking Launch Shaft Thrust Block Design

FIGURE 28.22 Frame analysis modeling of racking deformations ( Parsons Brinckerhoff, Inc. 1993, with permission). the free field. This magnification effect is not caused by the effect of dynamic amplification. Rather it is attributed to the fact that the ground has a cavity in it as opposed to the free-field condition. Determine the racking deformation of the structure, Ds, using the following relationship The seismic demand in terms of internal forces as well as material strains can be...

## 2910 Conclusions

The concept and method for design and analysis of glass panels is described in this chapter. The validity of the finite element formulation has been demonstrated for flat and curved panels with in-plane edge support flexibility. All these problems are related to the practical design of the glass system. Further, a summary of possible causes of breakage for glass panels is presented. It can be seen that, with a proper design and analysis method and methods of installation, glass structures can...

## 161 Analysis and Design of FRP Pultruded Structures 1611 Introduction

Truss structures and braced framed structures have been designed and constructed using thin-walled composite material fiber-reinforced polymer (FRP, commonly referred to as fiber-reinforced plastic) pultruded members for over 30 years. Pultruded structural members (referred to as pultrusions or pultruded shapes or pultruded profiles) have been used in a significant number of structures to-date, such as pedestrian bridges, vehicular bridges, building frames, stair towers, cooling towers, and...

## 2422 Type Choosing

In the preliminary stage of design, it is most important to choose an appropriate type of double-layer grid that will have direct influence on the overall cost and speed of construction. It should be determined comprehensively by considering the shape of building plan, size of span, supporting conditions, magnitude of loading, roof construction, and architectural requirements. In general, the system should be chosen so that the space grid is built of relatively long tension members and short...

## 105 Resistance Determination

The Load and Resistance Factor Design (LRFD) Manual for Engineered Wood Construction (American Forest and Paper Association 1996) distinguishes between nominal design values for visually and mechanically graded lumber connections and has supplements to provide guidance for all other wood-based products. This document provides both the reference design mechanical property and the applicable adjustment factors to account for end-use and environmental conditions. The reference properties that are...

## 6

Note that bearing on the gusset plate is more critical than bearing on the webs of the channels because the thickness of the gusset plate is less than the combined thickness of the double channels. Check bolt spacing The minimum bolt spacing is 3d 3(1) 3 in. The maximum bolt spacing is the smaller of 14t 14(0.303) 4.24 in. or 7 in. The actual spacing is 3 in., which falls within the range of 3 to 4.24 in., so bolt spacing is adequate. Check edge distance From...

## 005015

Source Prestressed Concrete Institute. Source Prestressed Concrete Institute. 8.5.5 Example 1 Prestress Losses in Beams A simply supported posttensioned 70-ft-span lightweight steam-cured double T-beam as shown in Figure 8.2 is prestressed by twelve 2-in. diameter (twelve 12.7 mm diameter) 270-K grade stress-relieved strands. The tendons are harped, and the eccentricity at midspan is 18.73 in. (476 mm) and at the end 12.98 in. (330 mm). Compute the prestress loss at the critical section in the...

## 315 Modifications to Alignment Charts

In using the alignment charts in Figure 31.4 and Equations 31.5 and 31.6, engineers must always be aware of the assumptions used in the development of these charts. When actual structural conditions differ from these assumptions, unrealistic design may result (Johnston 1976 Liew et al. 1991 Hajjar and White 1994 AISC 1999 Dafedar et al. 2001). The Structural Stability Research Council (SSRC) Guide (Johnston 1976) provides methods enabling engineers to make simple modifications of the charts for...

## Uqh

The allowable bearing strength of hollow spheres can be calculated by the following empirical formulas , t2 d2 1 , , Nc Zc( 6.6td - 2.2 K (tons) where D is the diameter of the hollow sphere (cm), t is the wall thickness of the hollow sphere (cm), d is the diameter of the tubular member (cm), s is the allowable tensile stress, zc and zt are the amplification factors due to the strengthening effect of the diaphragm, taken as 1.4 and 1.1, respectively, and K is a factor of safety. The Unibat...

## 251 Introduction

A bridge is a structure that crosses over a river, bay, or other obstruction and permits the smooth and safe passage of vehicles, trains, and pedestrians. An elevation view of a typical bridge is shown in Figure 25.1. A bridge structure can be divided into an upper part (the superstructure), which consists of the deck, the floor system, and the main trusses or girders, and a lower part (the substructure), which consists of piers, columns, footings, piles, and abutments. The superstructure...

## Gross Area Structural Engineering

Where Ag is the required gross area of the anchor, Fu is the minimum specified tensile strength, and f t 0.75 is the resistance factor for tensile fracture. 4.12.2.2 Limit State of Cone Pull-out From Figure 4.35, it is clear that the size of the cone is a function of the length of the anchor. Provided that there are sufficient edge distance and spacing between adjacent anchors, the amount of tensile force required to cause cone pull-out failure increases with the embedded length of the anchor....

## Bracing For Stability-state-of-the-art Yura University Of Texas At Austin

1 Winter, G. (1958), Lateral Bracing of Columns and Beams,'' Trans. ASCE, Vol. 125, Part 1, pp. 809-825. 2 Winter, G. (1960),''Lateral Bracing of Columns and Beams,'' Proc. ASCE, Vol. 84 (ST2), pp. 15611-1561-22. 3 Yura, J.A., Bracing, in Stability Design Criteria for Metal Structures, 5th Edition, Galambos, T.V. Ed. John Wiley & Sons, Inc., New York, 1998 Chapter 12. 4 Chen, S. and Tong, G. (1994), ''Design for Stability Correct Use of Braces,'' Steel Struct., J. Singapore Struct. Steel...

## Example 231

For the three-span continuous beam shown in Figure 23.10, all of the end-connections are semirigid except for the connection at joint D, which is rigid (r 1). The secant rotational stiffnesses of the semirigid connections associated with the serviceability and ultimate load states are 1.15 1010 and 5.75 x 109 Nmm rad, respectively. The beam is subjected to uniformly distributed dead and live loads, 3.2 and 12.0 kN m, respectively. The beam is laterally braced and has a W410 x 39 section with...

## Schwedler Dome Horizontal Polygonal Rings

A Schwedler dome also consists of meridional ribs connected together to a number of horizontal polygonal rings to stiffen the resulting structure so that it will be able to take unsymmetrical loads (Figure 24.14b). Each trapezium formed by intersecting meridional ribs with horizontal rings is subdivided into two triangles by a diagonal member. Sometimes the trapezium may also be subdivided by two cross-diagonal members. This type of dome was introduced by a German engineer J.W. Schwedler in...

## 20

The corresponding time effect factor is determined depending on which load combination is being considered. The most common application for sawn lumber, LVL, glulam timber structural composite lumber, and I-joists is to resist bending forces. In fact, since it is the most common application for dimensional timber members, the visual and machine stress-rated grading rules for lumber are developed around the concept that the members will be placed in bending about their strong axis. In this...

## 1823 Weak Clay

The problems encountered at soft clay sites include the amplification of the ground motion as well as vigorous soil movement that can damage foundations. Several bridges suffered collapse during the 1989 Loma Prieta Earthquake due to the poor performance of weak clay. Two parallel bridges were built in 1965 to carry Highway 1 over Struve Slough near Watsonville, CA. Each bridge was 800 ft long with spans ranging from 80 to 120 ft. The superstructures were continuous for several spans with...

## 2425 Cambering and Slope

Most double-layer grids are sufficiently stiff so that camber is often not required. Cambering is considered when the structure under load appears to be sagging and the deflection might be visually undesirable. It is suggested that the cambering be limited to of the shorter span. As shown in Figure 24.10, cambering is usually done in (a) cylindrical, (b) ridge, or (c) spherical shape. If the grid is being fabricated on site by welding, then almost any type of camber can be obtained as this is...

## 3 Kl

So, the component element buckling criterion is not a concern. Use 14 in. x 3 in. cover plates bolted to the flanges of the W24 x 229 section by in. diameter fully tightened bolts spaced 6 in. longitudinally. The design strength of a column can be increased if lateral braces are provided at intermediate points along its length in the buckled direction of the column. The AISC-LRFD Specification (1999) identifies two types of bracing systems for columns. A relative bracing system is one in which...

## Akp

Wall piers designed to resist 3 in 75-year induced elastic forces in transverse direction Plastic hinges at base of wall piers in weak direction Columns with moment reducing hinge details Plastic hinges at base of wall piers in weak direction Spread footings that meet 2 uplift criteria Seat abutments whose backwall is not designed to fuse, whose gap is not sufficient to accommodate the seismic movement, and which is designed for the expected impact force FIGURE 20.8 Permissible earthquake...

## 34321 Steel Plates and Shapes

AASHTO specifications for Grade 50 (minimum 350-MPa yield strength) bridge steel up to 38-mm thick require a CVN at a temperature that is 38 C greater than the minimum service temperature. The temperature shift accounts for the effect of strain rates, which are lower in the service loading of bridges (on the order of 10 3) than in the Charpy test (greater than 101). The temperature shift means that when a CVN is specified at some temperature, it ensures that the transition temperature for the...

## Wind Pressure Calculation For Curved Roof

FIGURE 24.17 Intersection and combination of cylindrical shells. FIGURE 24.19 Combination of cylindrical and spherical shells. FIGURE 24.19 Combination of cylindrical and spherical shells. 24.4.1 Design Loads 24.4.1.1 Dead Load The design dead load is established on the basis of the actual loads that may be expected to act on the structure of constant magnitude. The weight of various accessories cladding, supported lighting, heat and ventilation equipment and the weight of space frame comprise...

## 55 Computer Program

This section describes the practical advanced analysis program (PAAP) for two-dimensional steel frame design 6,19 . The program integrates the methods and techniques developed in Sections 5.2 and 5.3. The names of variables and arrays correspond as closely as possible to those used in theoretical derivations. The main objective of this section is to present an educational version of software to enable engineers and graduate students to perform planar frame analysis for a more realistic...

## 3112 Columns in Gable Frames

For a pin-based gable frame subjected to a uniformly distributed load on the rafter as shown in Figure 31.30a, Lu (1965) presented a graph (Figure 31.30b) to determine the effective length factors of columns. For frames having different member sizes for rafter and columns having (L h) of (f h) ratios not covered in Figure 31.30, an approximate method is available for determining K-factors of columns (Hansell 1964). The method is to find an equivalent portal frame whose span length is equal to...

## 279 Durability

Cooling tower shells, particularly in fossil fuel power plants, are subjected to a relatively severe environment over their lifetime, which may span several decades, and special care must be taken in order to provide a durable structure. The tower is subjected to the physical loads produced by wind, temperature, Compacted concrete Reinforced concrete in sheet piling box foundation FIGURE 27.54 Individual reinforced concrete foundation on concrete base. Compacted concrete Reinforced concrete in...

## Civil Engineering At

Where fcs is the stress in the concrete at the level of the centroid of the prestressing tendon. In general, this loss is a function of the stress in the concrete at the section being analyzed. In posttensioned, nonbonded members, the loss can be considered essentially uniform along the whole span. Hence, an average value of the concrete stress fcs between the anchorage points can be used for calculating the creep in posttensioned members. PHOTO 8.2 Prestressed concrete pretensioned T-beam...

## P

FIGURE 8.11 Strain distribution and curvature at controlling stages (a) initial prestress, (b) effective prestress after losses, (c) service load, and (d) limit state at failure 5 . FIGURE 8.11 Strain distribution and curvature at controlling stages (a) initial prestress, (b) effective prestress after losses, (c) service load, and (d) limit state at failure 5 . Use a plus sign for tensile strain and a minus sign for compressive strain. Figure 8.11c denotes the stress distribution for an...

## 250 20 250

FIGURE 25.56 Types of expansion joints (JASBC 1984) (a) blind slit type (b) slit plate type (c) angle joint type (d) postfitting butt type (e) rubber joint type (f) steel covered type (g) steel finger type (cantilevered) and (h) steel finger type (supported). FIGURE 25.56 Types of expansion joints (JASBC 1984) (a) blind slit type (b) slit plate type (c) angle joint type (d) postfitting butt type (e) rubber joint type (f) steel covered type (g) steel finger type (cantilevered) and (h) steel...

## Yves Malier Reference About High Performance Concrete

High-Performance Concrete,'' Modern Concrete Technology 5, E & FN SPON, London and New York, 591pp. 2 Malier, Y. 1990. Les beton a hautes performances,'' Du materiaux a l'ouvrage, Presses de l'Ecole Nationale des Ponts et Chaussees, Paris, France, 1990, 507pp. (English edition High Performance Concrete from Materials to Structure, Ed. by Yves Malier, E & FN SPON, 1992, 541pp.) 3 Zia, P., S.H., Ahmad, and Leming, M.L. 1996. High-Performance Concretes An Annotated...

## 2133 Design Response Spectra and Ground Motions

The selection of a performance objective, as just described, involves the specification of a hazard level. Unless ground motion time histories are used in a dynamic time-history analysis, it is customary to specify the hazard in terms of a response spectrum. The generation of the ground motion hazard spectrum is a function of several parameters, most of which pertain to site characteristics. Site-specific hazard analysis is recommended for very soft soils that are vulnerable to failure under...