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- A 100 mm x 200 mm wooden beam with a clear span of 7.2 m is embedded firmly ea one end and is simply supported on the other end as shown in the figure. If the allowable stresses are respectively 13.8 MPa and 1.11 MPa for bending and shear, ODetermine the safe maximum uniform load the beam can carry. Yeight of wood is 9.9 kN/m3 Find the reaction at B. OFind the max, moment of the beam.Light-grade steel channel was used as a purlin of a truss. The top chord of the truss is inclined I V: 4 H and distance between trusses is equal to 6 m. The purlin has a weight of 79 N/m and spaced at 1.2 m. on centers. The dead load including the roof materials is 720 Pa, live load of 1000 Pa and wind load of 1.2 1.2 1440 Pa. Coefficient of Purlins pressure at leeward and windward are 0.6 and 0.2 respectively. Assume all loads passes through the centroid of the section. Truss Properties of C 200 x 76 mm Sx = 6.19 x 104 mm Sy = 1.38 x 104 mm W = 79 N/m 12 12 1.2 I Allowable bending stress Fbx= Fby = 207 MPa Truss %3D 6m O Calculate the bending stress, fox, for dead load and live load combination (D+ L). Calculate the bending stress, foy, for dead load and live load combination (D + L). O Calculate the maximum ratio of actual to the allowable bending stress for load combination 0.75 (D + L + W) at the windward side. fbx = 151.14 MPa fby = 169.6 MPa Interaction = 1.25Light-grade steel channel was used as a purlin of a truss. The top chord of the truss is inclined I V : 4 H and distance between trusses is equal to 6 m. The purlin has a weight of 79 N/m and spaced at 1.2 m. on centers. The dead load including the roof materials is 720 Pa, live load of 1000 Pa and wind load of 1.2 1.2 1440 Pa. Coefficient of Purlins pressure at leeward and windward are 0.6 and 0.2 respectively. Assume all loads passes through the centroid of the section. Properties of C 200 x 76 mm Sx = 6.19 x 104 mm Sy = 1.38 x 104 mm3 W = 79 N/m 1.2 Truss 1.2 12 12 1.2 Allowable bending stress Fbr = Fby = 207 MPa Truss %3D 6m O Calculate the bending stress, fox, for dead load and live load combination (D + L). Calculate the bending stress, foy, for dead load and live load combination (D + L). O Calculate the maximum ratio of actual to the allowable bending stress for load combination 0.75 (D + L + W) at the windward side. fbx = 151.14 MPa fby = 169.6 MPa Interaction = 1.25
- Analyze completely the compound truss loaded as shwon below.04. Analyze completely the compound truss loaded as shwon below. D 24 kN 3 m E 2 m F 3 @ 4 m 12 PROBLEM 4 TABLE OF ANSWERS: МЕМBER NUMBER FORCE (k) AB 1 CD 2 EF 3 BC CF 5 BF 6 DE 7 AD 8 AE 9 4.The section of a Super-T prestressed concrete girder is shown below. The girder is simply supported on a span of 7.0 m and are pre-tensioned with total initial force of 825 kN from low-relaxation strands. The girder supports a total dead load of 2 kPa and live load of 6 kPa. There is a loss of prestress of 0.2 at service loads. Assume "-" for compression and "+" for tension. Hint: Assume tributary width is equal to flange width. Properties of the section: A = 100,000 mm2 INA = 940 x 106 mm4 All measurements in the drawings are in millimeters. 1. What is the stress, in MPa, at the top fibers of the girder at end span due to initial prestressing force only? 2. What is the stress, in MPa, at the bottom fibers of the girder at midspan due to initial prestressing force only? 3. What is the stress, in MPa, at the top fibers of the girder at end span due to prestressing force and service loads? 4. What is the stress, in MPa, at the bottom fibers of the girder at midspan due to prestressing…
- A composite beam has a simple span of 6 m. This consists of a Wide Flange steel section and a 12 mm concrete slab whose width is 1.5 m. Assume shoring was provided. | Wide Flange A = 9480 mm² D= 400 mm Unit Wt. = 23KN/m 1,= 270x10°mm* w= 0.74 KN/m | F,-138 MPa Concrete f~-20.7 MPa n=10 a) Determine the moment of inertia (transformed steel section) b) Compute the moment capacity of the composite beam. c) Compute the allowable live load moment of the composite beam.5 A T-shaped simply supported beam has the cross section shown in Figure P1.4. It has a spa (11 m), is loaded with a gravity live-load unit intensity W=2,500 plf (36.5 kN/), and is pre with twelve -in.-dia (twelve 12.7-mm-dia) seven-wire stress-relieved strands. Compute crete fiber stresses at service load by each of the following methods: (a) Basic concept (b) C-line (c) Load balancing Assume that the tendon eccentricity at midspan is e,= 9.6 in. (244 mm). Then given that S: - 5,000 psi (34.5 MPa) f. - 12V: - 849 psi (5.9 MPa) foe - 165.000 psi (1,138 MPa) : section properties are as follows: A -504 in² 1 = 37,059 in. - IJA. - 73.5 in. C, - 12.43 in. Wp - 525 pif e- 9.6 in. Apa - twelve in.-dia, seven-wire stress-relie S, - 2,981 in. S - 2,109 in. 1'-0 18 6 24LT30 ution#5 (to be typed here by the student) Solve all 3 partsS5. For the beam and loading shown in Figure 5.0, Design the cross section of the beam, knowing that the grade of timber used has an allowable bending stress of 170 MPа. 120 kN 60 kN b 2b 2 m 2 m 2 m
- Example 3 AT-shaped simply supported beam has the crass Section shown in Figure PL.4, It has a span of 36 t (11 m), is loaded with a gravity live-load unit intensily W, - 2,500 plt (365 kN), and is prestressed with twelve 1-in,-dia (Iweive 12.7-mm-dia) seven-wire stress-relieved strands. Compute the con- crete fiber stresses at service load le- 34 3 Mpa lei- 25 MPa e- 244 nn 1138 MPa The section properties: 25.4mm -MPa r-ly Ac- mm2 CA JI3.722 NT. 763 mm S- 4.885 ot 7 mn S 3.456e+7 rvr. Wp- 7.662 kN. (Including s.w) Hy- 36.5 kN/m Aps= 12 12.7 mwn (7 wire strands) (Answer: 10.5 MPa. 0.36MPa, 762mm 609 6 mmWhere is/are the location(s) of the maximum compressive flexural stress? A simple I-beam is loaded as shown. 20 mm P KN PKN P KN B 20 mm- B с D L/4 m L/4 m L/4 m Pin support at the NA Midspan at point B Mid span at point D Midspan at the top fiber Roller support at top fiber Section D at the top fiber Section C at +170 mm from the NA L/4 m 20 mm C 250 mm 150 mm 150 mm D AAbout Uncracked and Craked Section 1. A doubly reinforced beam has dimension of 300mmw x 600mmh. It is reinforced with 2-25mm diam compression bars and 4 25mm diam tension bars. Concrete cover from centroid of steel bar is 60mm. On its section has a bending moment of 300KN-m. Using working stress design method what are the stresses acting on the concrete, compressive and tensile steel bars? used n: 8