First we will find out the reaction at supports,
Take summition of forces in Y direction = 0
Ra + Rb = 12×3+ 0.5× 12 ×1.5
Now take moment about B = 0,
Ra×3 - 12×3×1.5 + 0.5×12×1.5×0.33× 1.5= 0
Therefore Ra = 17.5 KN
So, Rb= 27.5 KN
Now we will find out maximum bending moment in the beam
For that take a section at a distance of x from A
Therefore, Ra ×x- 12×x×0.5×x= Moment at X
To find out the value of at for maximum bending moment , differentiate this equation
So, Ra - 2×12×0.5×x = 0
From here X = 1.458
So bending moment at X= 1.458 is , 12.76 KN-m
Now we will use bending equation to find out required diameter
Bending equation is,
M/I= ¶/y
Where, M is bending moment which is equal to 12.76 KN-m
I is second moment of area which is equal to π×D^4/64
¶ is allowable bending stresses whose will is given as 150mpa
Y is distance of extreme fiber from neutral axis which is equal to D/2
Where D is diameter
So put the values in equation and get the value of diamete
12.76×10^6/(π×D^4/64)= 150/(D/2)
Therefore required diameter is 95.33 mm
solve with explansion please BONUS PROBLEM: Calculate the required diameter, d, of the bar if the...
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Wut unte. 02/06/2020, 12:00pm) Problem 1 (50 pts): For the beam shown, a) Determine the reaction forces at the supports b) Derive the loading, shear-force, and bending moment relationships (g(x), and c) Draw the V(x) and M(x) graphs and identify the locations of the maximum shear force and bending moment along the beam d) Determine the maximum tensile and compressive stresses e) Determine the maximum shear stress due to V 13 kN 50 mm --...
2. A rectangular beam, 400 x 600 mm gross dimension, is cast using a concrete strength of fc 30 MPa, reinforced with 5-25 mm diameter steel bar at the effective depth of 500 mm. If is subjected to a moment, M 130 kN-m. Determine the following: Magnitude of the bending moment that cracks the singly-reinforced beam section. (10 pts) b. For the computed cracking moment, determine the maximum compressive stress in the concrete and the stress in the tension steel....
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PROBLEM 3. A beam is to be made of steel that has an allowable bending stress of 165 MPa and an allowable shear stress of 100 MPa. Select an appropriate W shape that will carry the loading shown in Figure. 20 kN 20 kN/m
Design the cantilever beam below to take the maximum load. Calculate the load in KN to 2 decimal places, if the allowable bending stress is allow = 162 MPa and the allowable shear stress is Tallow = 95 MPa. Also I = 11.918 x 10-6 m4 and the y_bar = 0.04875 m from the top of the t-beam. 150 mm 15 mm T150 mm Hi 15 mm P P 2 m 2 m
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Problem #3: The rigid be m The rigid beam ACE is u sed the suspender bars. Bars AB der hars Bars AB and EF are made of aluminum and har CD is made of steel. Each barha and bar CD is made of steel Fach har has a cross-sectional area of 900 mm, Ex - 200 GPa, E-70 GPa P-20 KN. al 2 m 5 -15 Fox 190 0 3 FAQ +15 Foc 390...
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For the system shown in Figure (1), the bolt in C is subjected to a single shear and all other bolts are double shear. The diameter of bolt at C is 15 mm, diameter of bolt at D is 10mm and diameter of bolt A is 20mm. The allowable shear stress of bolt C is 200 MPa, allowable shear stress of bolt D is 150 MPa and allowable...
A concentrated load P is applied to the upper end of a 0.86-m-long pipe. The outside diameter of the pipe is D-106 mm and the inside diameter is d-98 mm. (a) Compute the value of Q for the pipe. (b) If the allowable shear stress for the pipe shape is 75 MPa, determine the maximum load P that can be applied to the cantilever beam. Answers: (a) Q = (b) P = kN
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4) The circular bar seen in the figure below is made of a brittle material with ultimate strengths in tension and compression of ou = 290 MPa and ou= 650 MPa, respectively. Let P = 30 N and T = 13 Nm. Using a factor of safety of 1.5 and the Maximum Principal Stress Theory, determine the minimum required diameter, d, to resist failure. (13 points) 1.25m 2.5m
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A solid steel bar of circular cross section has diameter d = 40 mm, length L = 1.3 m and shear modulus of elasticity G = 80 GPa. The bar is subjected to torques T acting at the ends. If the torques have magnitude T = 340 Nm, what is the maximum shear stress in the bar? What is the angle of twist between the ends? If the allowable shear stress is 42 MPa and the allowable angle of twist...