Structural Analysis

Q2 The portal frame carries vertical and horizontal forces as shown in the figure below. If Mp is equal to 40 kNm determine the upper and the lower load factors against collapse. Consider at least 2 combined mechanisms. 2 m 60 KN 2 m B E 2M₂ A 2 m 30 kN/m Mp 2 m с Mp D 2 m

Problem #4: GIVEN: Classroom portion of a 2-story school building in Portland, Oregon with interior columns spaced 35' apart in two perpendicular directions. Interior columns are the typical ones inside and not those closest to the outside of the building. Floor live loading is as specified in OSSC Table 1607.1. Roof live loading is 20 psf for this ordinary, flat roof per Table 1607.1. FIND: Total floor live load + roof live load (kips) for a single, typical interior column at (a) ground floor level, and (b) 2nd floor level. Consider live load reductions for both floor and roof. Draw both plan (looking down) and elevation (looking sideways) views of a portion of the building so you can better understand the problem. Reduce the floor live loads according to Section 1607.11.1 of the 2019 OSSC. This is similar to the discussion in the Hibbeler text. The Hibbeler text does not discuss the reduction of roof live loads, however they can be reduced, but using different methods than for floors. Do reduce the roof loads and use the roof load reductions described in OSSC Section 1607.13.2.1. Section 1607.13.1 indicates what to do if roof live loads are reduced to less than 20 psf and members being designed are continuous. Assume here that the beams are not continuous and are simply connected to the columns. Therefore, Section 1607.13.1 is not applicable, but 1607.13.2.1 is applicable to this problem. 7/10 Be sure to write out all of the calculations (checks) that you need to satisfy the provisions of the 2019 OSSC. This shows explicitly that you have considered all of the requirements and have not missed any of them. These are often inequalities that are specified in equation form or in words. Read the code carefully (every word) and don't skip over anything. This is very important in using building codes in general. Many of these checks are to see which equations are relevant to your situation.

Problem #5: GIVEN: Bend Senior High School in Bend, Oregon. Assume that it has an ordinary flat roof with roof drainage not constrained (roof is able to drain). FIND: Design snow load for the roof (psf). Notes: • Determine latitude/longitude of this location using Google Maps or Google Earth, for example. • Snow loads are determined using Section 1608 of the 2019 OSsc. • Information from the Snow Load Analysis for Oregon published by the Structural Engineers Association of Oregon can be obtained from: snowload.seao.org/lookup.html You need to cut and paste the address into your browser. • Obtain the design ground snow load from this site. Note that the longitude must be in negative degrees. • The Importance Factor for Snow Load, Is=1.10, as found in ASCE 7-16 Table 1.5-2. A secondary school is in Risk Category III (from OSSC Table 1604.5) if the (Group E) occupancy load is greater than 250. Sisters HS has approximately 550 students and faculty and staff. • For flat roofs, the design snow load (on the roof) is given by: a) Hibbeler Equation (1-5) (this is Eq. 7.3-1 in ASCE 7-16) b) C₂ = 0.9 (fully exposed roof in surface roughness B- urban area with numerous closely spaced obstructions) (Table 7.3-1 in ASCE 7-16). c) C₁ = 1.0 for heated building (Table 7.3-2 in ASCE 7-16) Also, read the Map Usage Notes (in the SEAO snow load site given above) on Minimum Roof Design Snow Load and apply these as well. If the minimum is greater than the value from Hibbeler Equation (1-5) (this is Eq. 7.3-1 in ASCE 7-16), then the minimum applies. Lastly, include the rain-on-snow surcharge load if appropriate. Fully. explain your logic in considering it.

Problem #6: GIVEN: One-story fire station planned near Florence, Oregon with a flat roof. Roof height = 12 ft. This critical facility is in Risk Category IV (from OSSC Table 1604.5). The building is rectangular and 50 ft. x 100 ft. in plan. It is situated right next to the beach, and the 100 ft dimension is parallel to the coast. It is considered to be enclosed per ASCE 7-16 Section 26.2. FIND: The controlling wind design pressures (combining external and internal pressures) to be used for the windward wall. These should be pressures for design of the main wind-force-resisting system (MWFRS) and not for the components and cladding. The MWFRS is composed of the walls and roof as they resist the wind as a complete structural system. Components and cladding are parts of the walls and roof as they resist the wind locally. SOLUTION NOTES: 1) Section 1609 of the 2019 OSSC covers wind loadings. It will be used in combination with appropriate sections in ASCE 7-16 that are briefly discussed in the Hibbeler text. The necessary information from ASCE 7-16 will be provided here. Individual MIV Set (Loadings): STRUCTURAL THEO (C6_381_001_F2022) 2) Use the 2019 OSSC to determine the Basic Design Wind Speed, V, for this location. 3) The Directional Procedure for MWFRS in an enclosed building is outlined in ASCE 7-16 Table 27.2-1. The definition of an enclosed building is provided in ASCE 7-16 Sections 26.2 and 26.12. 4) Velocity pressure exposure coefficient Kz = 1.03 for Exposure D (Table 26.10.1 in ASCE 7-16) for z ≤ 15 ft. Directionality factor, Kg = 0.85 (Table 26.6-1 in ASCE 7-16- note that this is different from the Hibbeler text). Topographic factor, Kat= 1.0 for flat terrain (ASCE 7-16 Section 26.8.2). Ground elevation factor, Ke=1.0 for sea level and to be conservative for all elevations. Gust effect factor, G=0.85 for rigid buildings and other structures. 5) Internal pressure coefficient for enclosed building is from ASCE 7-16 Table 26.13-1 or from the Hibbeler text. 6) Velocity pressure exposure coefficient, K₂ is from Table 28.10-1 in ASCE 7-16 or from wall pressure coefficient in Hibbeler. 7) Velocity Pressure qz or qn is from Eq. 28.10-1 in ASCE 7-16 or from the Hibbler text. 8) External pressure coefficient, Cp is from Fig. 27.3-1 in ASCE 7-18 or from the Hibbeler text. 9) Design wind pressure on the wall is given by Eq. 27.3-1 for a rigid building in ASCE 7-16 or in the Hibbeler text.

Q2: Determine the Force in member 1-3 of the steel truss shown in Figure 2, using Force Method. The stiffness EA is the same for all the members.

Q2: Determine the vertical displacement of joint 6 of the steel truss, shown in Figure 2, using Work-Energy principles and imaginary unit load. The cross- section area of each member is A= 200mm² and E=200GPa. Not: (a) Determine all required internal actions in the members using the pin- joint method or the method of sections C (b) You can use an Excel spreadsheet to calculate deflection once member forces are calculated. (c) Compare the deflection with Multiframe

Part C Given: y = 200 MPa all members - pefectly plastic (no hardening) Beams-Rectangular cross-sections: height=40cm, width = 20 cm Columns - Square cross-sections: height = 20cm 1. Using ANSYS, simulate the behavior of the frame shown for λ = 1, 1.25, 1.5, 1.75 and 2.0. Document your result by providing snapshots of the moment diagrams for A-1.25. Do all the simulations converge? 2. From the ANSYS results, identify the interval for the collapse load factor (I.E. between what 2 lambdas). 3. From the ANSYS simulations, identify where and in what sequence do the plastic hinges form. 4. Based on the location of the plastic hinges, use manual calculations to estimate the collapse load factor 5. Manually sketch the bending moment diagrams of beam DE at the collapse load

Question 3. Determine the internal normal force, shear force, and bending moment acting at point C in the beam.

F7-4. Determine the equation of the elastic curve for the beam using the x coordinate that is valid for ≤ ≤L, 2 and L,_ _ _≤L El is constant. Prob. F7-4

A square cross-section XXX mm beam, 2 metres long, is loaded from above in the middle with a load of Y=2 kN causing a compressive Bending Stress at the top of the beam. The beam i addition experiences a tensile end loading of Z=283 kN causing an End-Loading Stress, as illustrated in Figure Q9. Calculate the width and height of the beam to the nearest millimetre in order to reduce total stress at the top of beam to be near zero? Stating your answer to the nearest millimetre. X mm Z KN Load causing a compressive ing stress bending Y Y KN X mm, Square cross section Z Load causing end-loading tensile stress Figure Q9 Z KN I (5 marks)