DESIGN AND ANALYSIS OF SILO STRUCTURES Chapter four

March 21, 2015DESIGN AND ANALYSIS OF SILO STRUCTURES Chapter four

CHAPTER FOUR

PROGRAM APPLICATION

4.1 PROGRAM PROCEDUREThis chapter presents a brief description of the STAAD-PRO program developed by Bentley Company which governs the problem of analysis and design of in-plane structure (JOIST GIRDER) using Stiffness Matrix as Method (S.M.M.). It is consist of three major parts; first the analysis of the in-plane structure. Second part is the design of plate girder elements. Third part is the checking of joist girder elements stresses according to the AISC-89 Design Manual using ASD designing method.Based on theoretical equations presented in previous chapter, the following step-by-step procedure for the analysis of In-plane structures (Trusses) using Stiffness Matrix Method.The sign convention used in this analysis is as follow: the joint translations are considered positive when they act in positive direction of Y-axis, and joint rotations are considered positive when they rotate in counterclockwise direction:Prepare the analytical model of in-plane structure, as follows:1. Draw a line diagram of the in-plane structure (beam), and identify each joint member by a number. 2. Determine the origin of the global (X-Y) coordinate system (G.C.S.). It is usually located to the lower left joint, with the X and Y axes oriented in the horizontal (positive to the right) and vertical (positive upward) directions, respectively. 3. For each member, establish a local (x-y) coordinate system (L.C.S), with the left end (beginning) of the member, and the x and y axes oriented in the horizontal (positive to the right) and vertical (positive upward) directions, respectively.4. Number the degrees of freedom and restrained coordinates of the beam elements and nodes.5. Evaluate the Overall Stiffness Matrix [k], and Fixed-End forces Vector {Pf}. The number of rows & columns of [S] must be equal to the number of DOF of the structure. For each element of the in-plane structure, perform the following operations:a) Compute the Element stiffness matrix [ke] in (L.C.S) by apply the basic stiffness equation, as follow: a. .b) Transform the force vector form (L.C.S) to in (G.C.S.) using transformation matrix [A], as follow:a. .c) Transform the deformation vector form (L.C.S) to (G.C.S.) using transformation matrix [B], as follow: a. .d) It is evident that matrix [B] is the transpose of matrix [A], therefore ;a. .e) Substituting step (d) in step (a), resulting in: a. .f) Substituting step (e) in step (b), resulting in:a. .g) Inverting equation in step (f), resulting in: a. .h) Store the element stiffness matrix, in (G.C.S.), , for each element.6. Assemble Overall Stiffness Matrix [K] for the System of in-plane structure. By assembling the element stiffness matrices for each element in the in-plane structure, using their proper positions in the in-plane structure Stiffness Matrix [K], and it must be symmetric.7. Compute the Joint load vector {Pj} for each joint of the in-plane structure. 8. Determine the structure joint displacements {X}. Substitute {P}, {Pe}, and [K] into the structure stiffness relations, .and solve the resulting system of simultaneous equations for the unknown joint displacements {X}.9. Compute Element end displacement {e} and end forces {f}, and support reactions. For each Element of the beam, as following:10. Obtain Element end displacements {e} form the joint displacements {X}, using the Element code numbers.11. Compute Element end forces {f}, using the following relationship:

12. Using the Element code numbers, store the pertinent elements of {f}, in their proper position in the Support Reaction Vector {R}13. Check the calculation of the member end-forces and support reactions by applying the Equation of Equilibrium to the free body of the entire in-plane structure;,

4.3 STAAD-PRO PROGRAM APPLICATION:Two major case studies will be investigated to In the first case five different joist girder depth will be investigated starting form (72) to (80).

4.3.1. First Case study:Given A roof framing 36'-0" x 60"-0" bay (as shown bellow Figure). The following are the service loads:

Service Dead Load = 16 PSF Service Roof Live Load = 25 PSF Service Snow Load = 35 PSF Service Wind Uplift = -12 PSF

Required: design the joist girder that will carry a K series joist with maximum spacing of (6'-0") center to center (based on metal roof deck). Assume the joist (28K6) accessories weights is 10 PLF

Step 1: Determine joist girder depth and orientation:Assuming that the K series joist are distributed equally parallel to the short dirction (36, for higher strength) giving us a 10 even spaces (as shown bellow Figure).

Step 2: determine uniformly distributed service load (using ASD-IBC, load combinations):D + (W or 0.7E) + L + (Lr or S or R)Eq.(4.1)where: D = Dead Load = 6(16 PSF) + 10 PLF = 106 PLFLr = Roof Live Load = 6(25 PSF) = 150 PLFS = Snow Load = 6(35 PSF) = 210 PLFW = Wind Load = 6(-12 PSF) = -72 PLF

Applying Eq.(4.1), yields:D + (W or 0.7E) + L + (Lr or S or R)= 106 + 210 = 316 PLF

Step 3: Determine 28K6 joist end reactions:

Joist end reaction = wL / 2 = (316 PLF)(36'0") / 2 = 5688 lb. = 5.7 KIPS USE 6 kip

Step 4: depending on the provisions given by the SJI-2005(ASD) calculate the following: a) Determine number of actual joist spaces (N). In this Case, N = 10b) Compute (total service load) concentrated load at top chord panel points1. P = 6 kip.c) Select Joist Girder depth:I. Refer to the ASD Joist Girder Design Guide Weight Table for the 42'-0" span, 8 panel, 18.0K Joist Girder. The rule of about one inch of depth for each foot of span is a good compromise of limited depth and economy. Therefore, select a depth of 72 inches (slightly larger).

II. The Joist Girder will then be designated 72G10N6K JOIST GIRDER. Note that the letter K is included at the end of the designation to clearly indicate that this is a service load.III. The ASD Joist Girder Design Guide Weight Table shows the weight for a 72G10N6K as 35 PLF. AS it appear (35