M (kN.m)e.V (kN)A cantilevered beam has of length L = 10 m and is subjected to a vertical load P₁ = 50 kN, an axialload P₂ = 100 kN passing through the neutral axis, a moment M = 200 kN.m, and a uniformlydistributed load w = 30 kN/m, as shown. The cross-sectional view and dimensions are illustratedbelow, with point C representing the centroid of the cross-section.300 mmWP₁ولا25 mmNeutral Axis200 mmAxDP2MSupport Material50 mmSTRESS FORMULATION25 mmN2Normal stress:σN=Beam's cross-sectionM₂yL (m)Bending stress:ΤρTorsional shear stress:T=d.Draw the shear force diagram for the beam. Show all your work.V, QTransverse shear stress:T=Q=YA'orQ=PW1₂tBEAM SIGN CONVENTIONVVtywL(m)Neutral AxisPzM(w):Positive internal shearM MPositive internal momentBeam sign conventionCROSS-SECTIONAL MOMENTS OF INERTIA ABOUT THE CENTROIDybh³Quadratic (second)1, =l₁ =moment of inertia12hb312πρ1₂ = ly=4Polar moment ofinertia1x =bh3+hb312πρDraw the bending moment diagram for the beam. Show all your work.P₁Centroid location:Parallel axis theorem:Σχιλι= Al1c ==Σ (1c₁ + A₁ d₁²)AL42DL (m)Neutral AxisP₂Mx (m)

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Answered: M (kN.m) e. V (kN) A cantilevered beam…

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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The cantilever beam shown in the figure consists of a rectangular structural steel tube shape [E = 200 GPa;I = 95 × 10° mm*). For the loading shown, determine the beam deflection at point B. Assume PB = 14 kN, Pc = 50 kN, wAB 65 kN/m 16 kN/m, L1 1.5 m, and L2 = 3.0 m. ,WBC APB Pc WAB WBC B |C L, L, i mm VB =
4.
6b
Question 3 A compound beam is connected by a pin at B, and a pin in a slot at C, and loaded as shown. Couple moment M = 500 N.m, force F= 2500 N, the triangular distributed load has a peak intensity w = 1200 N/m. Force F acts at an angle 0 = 60°, while the beam dimensions are such that a= 1.0 m, b = 0.5 m, c = 1.0 m, d= 1.5 m, e = 1.0 m, f= 2.0 m, and g= 1.0 m. M while E D Determine: a) the horizontal and vertical components of the pin reactions at B and C, and b) the normal force, shear force, and bending moment acting at point F of the beam.
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100 N/m, A simply supported beam ABCD is subjected to a linearly distributed load, with wo two concentrated loads, one at C and the other at D, and a point moment at B as shown in Figure 4.1. The angles of the point loads are: 0₁ = 40° and 0₂ = 30° and the dimensions are a = = 5 m, b = 3 m and c = 2 m. b) Use the method of sections to derive expressions for the internal resultant loadings, i.e., normal (N) and shear (V) forces as well as bending moment (M) at the cross-section of the beam as functions of x. The expressions must be valid for 0≤x≤a and a ≤x≤ b and b≤x≤c. Check that your equations provide values at the midpoint of AB that are consistent with your results in part a. Wo A X a B 1 500 N 의 200 N·m b Figure 4.1. - Simply supported beam 0₂ 2 300 N
Consider the beam shown in (Figure 1). Suppose that P = 6 kip, w = 1.2 kip/ft. Point E is just to the right of the 6-kip load. Follow the sign convention. Figure -6 ft + D 6 ft W B 4 ft- E -4 ft T 1 of 1 Part D Determine the normal force at section passing through point E. Express your answer to three significant figures and include the appropriate units. NE = Submit Part E VE = Submit Part F Determine the shear force at section passing through point E. Express your answer to three significant figures and include the appropriate units. Value ME = Request Answer Submit Value Request Answer Units Determine the moment at section passing through point E. Express your answer to three significant figures and include the appropriate units. Value Request Answer Units ? Units
Consider the beam shown in (Figure 1). Suppose that P = 6 kip, w = 1.2 kip/ft. Point E is just to the right of the 6-kip load. Follow the sign convention. Figure -6 ft + D 6 ft W B 4 ft- E -4 ft T 1 of 1 Part A Determine the normal force at section passing through point D. Express your answer to three significant figures and include the appropriate units. ND = Submit Part B VD = Submit Determine the shear force at section passing through point D. Express your answer to three significant figures and include the appropriate units. Part C Value MD Request Answer = Value Request Answer Determine the moment at section passing through point D. Express your answer to three significant figures and include the appropriate units. ULA Units Value Submit Request Answer Units ? Units ?
A simple beam of length L = 5 m carries a uniform load of intensity q = 5.8 kN/m and a concentrated load 22.5 kN (see figure). P = 22.5 kN 1.5 m q = 5.8 kN/m -L 5 m- The 1-1 and 2-2 axes are labeled on the cross section below. (a) Assuming oalow = 120 MPa, calculate the required section modulus S (in mm). (At this point, disregard the weight of the beam.) Select the most economical wide-flange beam (W shape) from this table, and recalculate S (in mm), taking into account the weight of the beam. Select a new beam if necessary. mm3 What is the suitable beam size? O w 360 x 79 w 200 x 31.3 O w 360 x 39 O w 250 x 89 O w 200 x 41.7
The continuous beam shown in the diagram has lengths L1=5 m and L2=4 m. The beam is subjected to a uniformly distributed load q = 4 kN/m which start at a distance b= 0.1*L2 m from the support B and extend to a distance c=0.4*L, m beyond the starting point and a point load P = 9 kN located at a distance a = 0.1*L, m from support A. What is the value of the bending moment at the middle of the span AB if the beam is inclined at an angle 0=20 degree. Give your answer to one decimal place. a L1 L2
A cantilever beam carries a trapezoidaldistributed load (see figure). Let wB = 2.5 kN/m,wA = 5.0 kN/m, and L = 2.5 m. The beam has amodulus E = 45GPa and a rectangular cross sectionwith width b = 200 mm and depth h = 300 mm.Use the method of superposition and Cases 1 and8 in Table H-1 to calculate the def lection and rotationat B.
A 300 mm x 125 mm I-beam has flanges 13 mm thick and web 8.5 mm thick. Calculate the shape factor and the moment of resistance in the fully plastic state. Take бy = 250 MN/m2 and Ixx = 85 x 10-6 m4.

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