Question

A beam is of T section, as shown in fig. The beam is simply supported over a span of 4m and carries a UDL of (1.7+Your R...


A beam is of T section, as shown in fig. The beam is simply supported over a span of 4m and
carries a UDL of (1.7+Your Roll No.) kN/m run over the entire span. Determine the maximum
tensile and maximum compressive stress.

Answer

Given,

UDL w = (1.7 + Roll number ) kN/m

L = 4 m

Support = Simply supported

Centroid (NA) ,

Mechanical Engineering homework question answer, step 2, image 1

x=0y=y1A1+y2A2A1+A2y=175(7500)+75(7500)7500+7500y=125 mm

 

 

Moment of Inertia,

I=I1+I2I=150(50)312+(150)(50)(175-75)2]+[50(150)312+(150)(50)(125-75)2] I=1562500+7.5×107+1.40625×107+1.875×107I=1.09375×108 mm4

 

Maximum Moment,

Suppose your roll number is 1 .

w=1.7+1w=2.7 kN/mMmax=(2700)(4)28Mmax=5400 NmMmax=5400×103 Nmm

Maximum Compressive Stress and Tensile stress is at Top fiber and bottom fiber respectively.

σC=Mmax(200-125)IσC=5400×103(200-125)1.09375×108σC=0.049(200-125)σC=3.675 MPa  (Mangitude)σT=5400000(125)1.09375×108σT=6.171 MPa

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