A1 Present the shear force and bending moment diagrams of the following beams and frames (Figure A1). There is no need to consider the buckling of any compression members. No calculation is required. P kN P kN Figure A1 (a): Cantilever beam encastrated at point A and subjected to 2 point loads P (kN)

A1 Present the shear force and bending moment diagrams of the following beams and frames (Figure A1). There is no need to consider the buckling of any compression members. No calculation is required. P kN P kN Figure A1 (a): Cantilever beam encastrated at point A and subjected to 2 point loads P (kN)

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question (1): A rectangular beam has a width b = 400 mm, and effective depth d = 850 mm and a total height h = 900 mm. The beam is subjected to an ultimate moment Mu = 1500 kN.m and an ultimate shear force Vu = 700 kN. 1- ) Design the beam for flexure to calculate the required area of steel. 2-) Using stirrups Φ 10 mm ( No.10) diameter, calculate the required spacing (s) between the stirrups at the ultimate shear force section. For all questions, Use f’c= 28 MPa and Fy= 420 MPa
Situation 11 An overhang beam is loaded as shown below. The beam cross-section was built by attaching two (2) channels to a 9mm thick plate using 16mm rivets The property of the channel is given: Depth, D=225 mm Flange Width, B=112.5 mm. Flange Thickness, tf=9mm Web Thickness, tw9 mm The allowable flexural stress on the beam is 180 MPa. Rivets has a capacity of t 100 MPa on shear, for bearing, o.-200 MPa on single sheer, a-260MPa on double shear Determine the location of centroid, y, from top of the beam in mm Determine the moment of inertia, I, of the section in mm^4. Determine the maximum allowable moment, M(all) in kn-m, base on the beam's cross-section. Determine the location of the maximum moment on the beam in meters. Determine the maximum moment, in kN-m, on the beam Determine the maximum flexural stress on the beam in MPa.
Situation 11. An overhang beam is loaded as shown below. The beam cross-section was built by attaching two (2) channels to a 9mm thick plate using 16mm rivets The property of the channel is given below: Depth, D=225 mm Flange Width, Bf=112.5 mm. Flange Thickness, tf=9mm Web Thickness, tw=9 mm The allowable flexural stress on the beam is 180 MPa. Rivets has a capacity of τ= 100 MPa on shear, for bearing, σb=200 MPa on single sheer, σb= 260MPa on double shear. 3. Determine the maximum allowable moment, M(all) in kn-m, base on the beam's cross-section. 4. Determine the location of the maximum moment on the beam in meters.
Situation 11. An overhang beam is loaded as shown below. The beam cross-section was built by attaching two (2) channels to a 9mm thick plate using 16mm rivets The property of the channel is given below: Depth, D=225 mm Flange Width, Bf=112.5 mm. Flange Thickness, tf=9mm Web Thickness, tw=9 mm The allowable flexural stress on the beam is 180 MPa. Rivets has a capacity of τ= 100 MPa on shear, for bearing, σb=200 MPa on single sheer, σb= 260MPa on double shear. 7. Determine the maximum shearing stress on the beam in MPa. 8. Determine the flexural stress, In MPa, on the fiber 30mm above NA at distance 1m from A
A W 360 x 44 of A992 steel column (Fy =345 MPa) having a length of 4m is fixed at both ends. Compute the effective width, be, of the slender web.Compute the value of reduction factor, Q, due to slender elementsin compression members.Compute the nominal compressive strength of the W-section.Properties of W 360 x 44Ag = 5710 mm2d = 351 mmbf = 171 mmtf = 9.78 mm tw = 6.86 mmkdes = 19.9 mmk1 = 19.1 mmrx = 146 mmry = 37.8 mm
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For the given loads F1=42 KN, F2=48 KN, F3=45 KN, F4=32 KN (Assume internal forces are in tension) 1- Magnitude of reaction at K is (KN) :(a. 151 - b. 226.5 - c. 302 - d. 377.5 - e. 453 ) 2- internal force in member JH (KN) :(a. -327 - b. -218 - c. -436 - d. -545 - e. -654) 3- internal force in member IH (KN) : (a. -204.600222 - b. -136.400148 - c. -272.800296 - d. -341.00037 - e. -409.200444 ) 4- Magnitude of reaction at A is (KN) 5- internal force in member IK (KN) is 6- internal force in member GF (KN)
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Situation 11 An overhang beam is loaded as shown below. The beam cross-section was built by attaching two (2) channels to a 9mm thick plate using 16mm rivets The property of the channel is given below: Depth, D=225 mm Flange Width, B=112.5 mm. Flange Thickness, tf=9mm Web Thickness, tw9 mm The allowable flexural stress on the beam is 180 MPa. Rivets has a capacity of t 100 MPa on shear, for bearing, o.-200 MPa on single sheer, a-260MPa on double shear. Determine the maximum flexural stress on the beam in MPa. Determine the maximum shearing stress on the beam in MPa.
The rectangular beam with a span length of 7.2 m has an effective depth, d = 430mm and a width of 250mm. It has 2-legged 10mmØ stirrups spaced at 130 mm on centers all throughout the beam length. Determine the maximum wu that the beam can carry based on the shear capacity of the beam. Use fc' = 21MPa and Grade 40 rebars. a. Adopt smaller of S' : S'1 = Avfy / (0.062b√f'c) S'2 = Avfy / (0.35b) b. S" = (0.062/0.33) / S'1 c. 1. if S > S' ; ØVn = Ø 0.5Vc 2. if S"<S<S' ; Smax = least of S' or d/2 or 600mm i. S> Smax ; ØVn = Ø 0.5Vc ii. S< Smax ; ØVn = Ø (Vc + ( Avfyd / S ) ) 3. if S < S" ; Smax = least of S' or d/4 or 300mm i. S> Smax ; Vs = 0.33√f'c bwd ØVn = Ø (Vc + 0.33√f'c bwd) ii. S< Smax ; ØVn = Ø (Vc + ( Avfyd / S ) ) Find: 1. Vc 2. s' and s'' 3. smax 4. ØVn 5. Wu
A 300mm by 600mm rectangular beam is subjected to uniform ultimate load of Wu=200kN/m over the whole span. The beam is simply supported over a span of 4m. The reinforcements are 2-28 mm diameter compression reinforcement and 4-28 mm diameter tension reinforcement. Use f'c=21MPa, fy=415MPa, stirrups=10mm, and cc=40mm. Calculate the maximum positive moment in the beam in kN.m.0 Calculate the depth of compression block in the beam in mm.0 Calculate the stress in the compression compression reinforcement in MPa.0 Calculate the ultimate moment capacity of the beam section in kN.m.0
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