Question

5.8-3 A simply supported wood beam is subjected to uniformly distributed load q. The width of the beam is 150 mm and the height is 200 mm. Determine the nor- mal stress and the shear stress at point C. Show these stresses on a sketch of a stress element at point C q =5.8 kN/m 75 mm С B A Μ 1 m 3 m 200 mm Z 150 mm PROBLEM 5.8-3

I want problem solving

Answer 1

Normal Stress at point C = 1.45 MPa

Shear Stress at point C = 0.35 MPa

The leam is undur bemding rm he wnijonmly wn disbubulid ad Thore villk Jending shus and Shiar Shass al homt c lecause Fitsl we will ind Reactuons af point A ond C ond find gorural -vapvession for Ia Force and Bending omoht belng a at Becleon leam V-5-8 KN AM The Radcliem af hoimt A omd Ban 2-dvadlien is geng Lsecaueo thare is no orligernal dusarane n W-dinacligm RD FBD Beam Equwalont Iead acts at mid pamt ef lengh AB Drafenaly dubraluird Saecalon egh onuich Ba UDL Equvalont Load, 8= 5-8x3 Fquwialonk Lood Brahflind y acts A=17-4 KM 8-17.4 1.5 1.5 B Re ef Beam Showng Equisalet Load The Beam is in Stalio Equilibeun under he acion of Load We will use tblie Equlilrium Bqualion to elue gor wnkneum ors, FBD Momond about any feint goue fora static AStali Egulirum We will take Momont alout hoint A, MMA=O

17-4x 1-5 Rex3 -0 Re orakes Caarasir Clookeuwese Monmant Rences Clockitrse Momant Ra= 8.7 KN im Sihe Equilibrium Son a byolams Rat Re-17-4 =O Ra-17-4-8-7 RA=8.7KN FBD of Leff Saoluen Beam Shousing Equsabucd Lood Dnifionrdy disimabutod Lood Re=8-7 9% Th: Sign CenuRentuen fer wling Shoan Fere Equalonat homt X, Thaar fence lean s takom hesliuse Shoar fere in dovonend daeclion on fe sclon of Sheawon 'us taken nagaluve Sign aonuventuen fer wardliry Marond qulen abeut Aouint x Clodbwiwe mambpn (Sgging Mamoal) sbkon frestve on of Sucliery Counlen cleckwise Momend gi Mmand s laken Wyaluve Bife Sachon

Vs-RA-9UM Genwal Equaliuon of Shoamn lerce a Opy Sacluen at &dislanee from Piadurit A Vr=8.7-5.8X M=RAX-9%- Me= 8-72-5.822Gonnal Equalan of Bending Momand af 2 f3mt A Rord Shoan ferce omd Benduing Memonl at fomt C, sukeltat X=1AUM Equalion of Shar forci and Berding Mamant Ve=-8.7-5.8 Ve 2-g KN Mc- (8-7x1)-(5.81) Me=5.8 KN-M Me-5-8x10 N-mm The Wonmal Shrass at prent c wll le due o londng ur uoill use rd Bonding Equalen io tomali Thndena Benduing stroas at c. whare Me is he banding memonl af Cress Sacluon I 2nd Memont of asan aboul Nautral Aris idance& fent rem Neulral Aus 176 200 Weubral Axus 25 In ths Case 3-aris is the neubral anis The fount Cis in emfression because k150 b im

T-I bhs Erussion for Momont oR Anarlia Cshere h dohth o Loam beam I I(15000 b Width of T= 108 MmA Ye = .25 Mz-Me- 58X10 N-mm Sule hitak Bra value im Bending Bualion 25 x5-8x10 I 08 V=l0 45 MPa Wenmal Strars af Psint C The Genral Exdrassion or Shoah bass at Sectien x-x ond at a distome y grom Neuthal Aris ora Ratangulan Cress-Saclun is, ahe same as bhs phonluogud i Rondwing Eaualaon h=200 b=150 y-ye= 25Mm Rgusatuen an be Atarad un ony 3hrangth of Malertal Tex book bh3 Te= 6x2-903 (2001- 95 150x2003 Shear Stress af Pent C Te= 0.135 MPa The Sliaess Elomont af foint C,